Julius Robert Oppenheimer Archive (PDF Library)

J. Robert
Oppenheimer
Science and the
Common
Understanding

4h

SCIENTIFIC— General Science

The 1953 Reith Lectures, delivered over the B.B.C. from London, were
directed by Professor Oppenheimer to an examination of “what there
is new in atomic physics that is relevant, helpful, and inspiriting for
men to know.” This led him, he says, into a relatively quiet room, that
we know as quantum theory or atomic theory, in the house called
“science.”

“It is a vast house indeed. It does not appear to have been built upon
any plan but to have grown as a great city grows. There is no central
chamber, no one corridor from which all the others debouch. All about
the periphery men are at work studying the vast reaches of space and
the state of affairs billions of years ago; studying the intricate and
subtle but wonderfully meet mechanisms by which life proliferates,
alters and endures; studying the reach of the mind and its ways of
learning; digging deep into the atoms and their unfathomed order. It is
a house so vast that none of us know it, and even the most fortunate
have seen most rooms only from the outside or by a fleeting passage,
as in a king's palace open to visitors. It is a house so vast that there is
not and need not be complete concurrence on where its chambers
stop and those of the neighboring mansions begin.

“It is not arranged in a line nor a square nor a circle nor a pyramid,
but with a wonderful randomness suggestive of unending growth and
improvisation. Not many people live in the house, relatively speaking—
perhaps if we count all its chambers and take residence requirements
quite lightly, one tenth of one per cent of all the people in this world—
probably, by any reasonable definition, far fewer. And even those
live elsewhere also, live in houses where the rooms are not lab =
atomic theory or genetics or the internal constitution of the stars

=

quite different names like power and production and evil and Sy =
and history and children and the word of God. ——
“We go in and out; even the most assiduous of us is not bound tt€@ =
vast structure. One thing we find throughout the house: there ar =
locks; there are no shut doors; wherever we go there are the signs =
usually the words of welcome. It is an open house, open to all comes =
--

design: WARD & SAKS

Science and the

Common Understanding

J. ROBERT OPPENHEIMER

Simon and Schuster

New York

ALL RIGHTS RESERVED
INCLUDING THE RIGHT OF REPRODUCTION
IN WHOLE OR IN PART IN ANY FORM
COPYRIGHT, 1953, 1954, BY J. ROBERT OPPENHEIMER
PUBLISHED BY SIMON AND SCHUSTER, INC.
ROCKEFELLER CENTER, 630 FIFTH AVENUE
NEW YORK 20, N. Y.

FIRST PAPERBACK PRINTING, 1966

Library of Congress Catalog Card Number: 54-8650
Dewey Decimal Classification Number: 530.1

CONTENTS

1
NEWTON: THE PATH OF LIGHT 3
2
SCIENCE AS ACTION: RUTHERFORD’S WORLD 20
3
A SCIENCE IN CHANGE 35
4
ATOM AND VOID IN THE THIRD MILLENNIUM 51
5
UNCOMMON SENSE 68
6
THE SCIENCES AND MAN’S COMMUNITY 83
APPENDIX I 101
118

APPENDIX II

Science and the

Common Understanding

NEWTON:

THE PATH OF LIGHT

SCIENCE has changed the conditions of man’s life.
It has changed its material conditions; by changing them
it has altered our labor and our rest, our power, and the
limits of that power, as men and as communities of men,
the means and instruments as well as the substance of our
learning, the terms and the form in which decisions of
right and wrong come before us. It has altered the com-
munities in which we live and cherish, learn and act. It has
brought an acute and pervasive sense of change itself into
our own life’s span. The ideas of science have changed the
way men think of themselves and of the world.

The description of these changes is not simple; it is rich
in opportunity for error. As for the great material changes
which science and practical art have made possible—ma-
chines, for instance, or power, the preservation of life, the
urbanization of populations, new instruments of war, new
means of communication and information—these are but

4 SCIENCE AND THE COMMON UNDERSTANDING

part of the materials for the analysis of political economy
and the wisdom and the insight of history. These are
strands in the tangled affairs of men, and their evaluation
is no more likely to be final and exhaustive than in any
other part of history.

As for the more direct effects of discovery in science on
the way men think about things which are not themselves
part of science, the historian of ideas has a similar prob-
lem. Noting what in actual fact men have said about what
they thought, who it was that thought it, and why he
thought it, one finds, as in all history, that the contingent
and the unpredictable, the peculiar greatnesses and blind-
nesses of individual men play a determining part. One
even finds the science of great scientists taken in the name
of those scientists for views and attitudes wholly foreign
and sometimes wholly repugnant to them. Both Einstein
and Newton created syntheses and insight so compelling
and so grand that they induced in professional philoso-
phers a great stir of not always convenient readjustment.
Yet the belief in physical progress, the bright gaiety, and
the relative indifference to religion characteristic of the
enlightenment, were as foreign to Newton’s character and
preoccupation as could be; this did not keep the men of
the enlightenment from regarding Newton as their patron
and prophet. The philosophers and popularizers who have
mistaken relativity for the doctrine of relativism have con-
strued Einstein’s great works as reducing the objectivity,
firmness, and consonance to law of the physical world,
whereas it is clear that Einstein has seen in his theories of

NEWTON: THE PATH OF LIGHT §

relativity only a further confirmation of Spinoza’s view
that it is man’s highest function to know and to understand
the objective world and its laws.

Often the very fact that the words of science are the
same as those of our common life and tongue can be more
misleading than enlightening, more frustrating to under-
standing than recognizably technical jargon. For the
words of science—relativity, if you will, or atom, or muta-
tion, or action—have been given a refinement, a precision,
and in the end a wholly altered meaning.

Thus we may well be cautious if we inquire as to
whether there are direct connections, and if so of what
sort, between the truths that science uncovers and the way
men think about things in general—their metaphysics—
their ideas about what is real and what is primary; their
epistemology—their understanding of what makes human
knowledge; their ethics—their ways of thinking, talking,
judging, and acting in human problems of right and
wrong, of good and evil.

These relations, the relations between scientific findings
and man’s general views, are indeed deep, intimate, and
subtle. If I did not believe that, I should hardly be ad-
dressing these lectures to an attempt to elucidate what
there is new in atomic physics that is relevant, helpful,
and inspiring for men to know; but the relations are not,
I think, relations of logical necessity. This is because sci-
ence itself is, if not an unmetaphysical, at least a non-
metaphysical activity. It takes common sense for granted
as well as most of what has gone before in the specialized

6 SCIENCE AND THE COMMON UNDERSTANDING

sciences, And where it adds, alters, or upsets, it does so on
the basis of an uncritical acceptance of a great deal else.
Thus, to the irritation of many, the assertions of science
tend to keep away from the use of words like “‘real”’ and
“ultimate.” The special circumstances of the discovery of
scientific truth are never very far from our minds when
we expound it, and they act as a protecting sheath against
their unlimited and universal acceptance. A few illustra-
tions may make this clearer.

We have discovered atoms. In many ways they act like
the atoms of the atomists. They are the stuff of which mat-
ter is made; their constellation and motion account for
much—in fact, for most of the ordinarily observable prop-
erties of matter. But neither they nor the smaller, less
composite particles of which they are made are either per-
manent, unchanging, or unchangeable. They do not act
like objects of fixed form and infinite hardness. Such find-
ings may be persuasive in discouraging the view that the
world is made of fixed, immutable, infinitely hard little
spheres and other shapes; but such findings are not in the
nature of things conclusive, for one may always hold that
the true atoms, the immutable, hard atoms, have so far
eluded physical discovery, but that they are nevertheless
there, and only when they are found will physics be deal-
ing with the ultimate reality. Beyond that, one can hold
that, although they may never be found by physical ex-
periment, they are the underlying reality in terms of which

NEWTON: THE PATH OF LIGHT 7

all else, including the world of physics, is to be under-
stood.

Or, again, we may have discovered that as the nervous
impulses pass from the retina of the eye toward the brain
itself their geometric disposition resembles less and less
that of the object seen. This may complicate or qualify the
view that the idea is a geometric replica of the object of
vision. It cannot and need not wholly exorcise it.

The scientist may be aware that, whatever his findings,
and indeed whatever his field of study, his search for truth
is based on communication with other people, on agree-
ment as to results of observation and experiment, and on
talking in a common tongue about the instruments and ap-
paratus and objects and procedures which he and others
use. He may be aware of the fact that he has learned al-
most everything he knows from the books and the deeds
and talk of other people; and, in so far as these experi-
ences are vivid to him and he is a thoughtful man, he may
be hesitant to think that only his own consciousness is real
and all else illusion. But that view, too, is not by logic
exorcised; from time to time it may rule his spirit.

Although any science gives countless examples of the
interrelation of general law and changing phenomena, and
although the progress of science has much to do with the
enrichment of these relations, knowledge of science and
practice of it and interest in it neither compel nor deny the
belief that the changing phenomena of the actual world
are illusion, that only the unchanging and permanent
ideas are real.

8 SCIENCE AND THE COMMON UNDERSTANDING

If, in the atomic world, we have learned—as we have
learned—that events are not causally determined by a
strict, efficient, or formal cause; if we have learned to live
with this and yet to recognize that for all of the common
experience with ordinary bodies and ordinary happenings
this atomic lack of causality is of no consequence and no
moment, neither the one finding nor the other ensures that
men when they think of the world at large are bound to a
causal or a non-causal way of thinking.

These many examples show that there can indeed be
conflict between the findings of science and what a philoso-
pher or a school of philosophy has said in great particular
about some part of experience now accessible to science.
But they also show that, if there are relationships between
what the sciences reveal about the world and how men
think about those parts of it either not yet or never to be
explored by science, these are not relationships of logical
necessity; they are not relationships which are absolute
and compelling, and they are not of such a character that
the unity and coherence of an intellectual community can
be based wholly upon it.

But if these examples indicate, as we should indeed ex-
pect from the nature and conditions of scientific inquiry,
that what science finds does not and cannot uniquely deter-
mine what men think of as real and as important, they must
show as well that there is a kind of relevance—a relevance
which will appear different to different men and which
will be responsive to many influences outside the work of
science. This relevance is a kind of analogy, often of great

NEWTON: THE PATH OF LIGHT 9

depth and scope, in which views which have been created
or substantiated in some scientific enterprise are similar
to those which might be held with regard to metaphysical,
epistemological, political, or ethical problems. The suc-
cess of a critical and sceptical approach in science may en-
courage a sceptical approach in politics or in ethics; the
discovery of an immensely successful theory of great
scope may encourage the quest for a simplified view of
human institutions. The example of rapid progress in un-
derstanding may lead men to conclude that the root of evil
is ignorance and that ignorance can be ended.

All these things have happened and all surely will hap-
pen again. This means that, if we are to take heart from
any beneficent influence that science may have for the
common understanding, we need to do so both with mod-
esty and with a full awareness that these relationships are
not inevitably and inexorably for man’s good.

It is my thesis that generally the new things we have
learned in science, and specifically what we have learned
in atomic physics, do provide us with valid and relevant
and greatly needed analogies to human problems lying
outside the present domain of science or its present bor-
derlands. Before I talk of what is new I shall need to
sketch, with perhaps an exaggerated simplicity and con-
trast, the state of knowledge and belief to which these cor-
rectives may apply. In doing this, we may have in mind
that the general notions about human understanding and
community which are illustrated by discoveries in atomic
physics are not in the nature of things wholly unfamiliar,

10 SCIENCE AND THE COMMON UNDERSTANDING

wholly unheard of, or new. Even in our own culture they
have a history, and in Buddhist and Hindu thought a more
considerable and central place. What we shall find is an
exemplification, an encouragement, and a refinement of
old wisdom. We shall not need to debate whether, so
altered, it is old or new.

There are, then, two sketches that I would like to draw
of the background for the altered experience of this cen-
tury. One is the picture of the physical world that began
to take shape in the years between Descartes’ birth and
Newton’s death, that persisted through the eighteenth cen-
tury, and with immense enrichments and extensions still
was the basic picture at the beginning of our own.

The second sketch has to do with the methods, the hopes,
the program, and the style which seventeenth- and eight-
eenth-century science induced in men of learning and in
men of affairs, with some of the special traits of that pe-
riod of enlightenment which we recognize today as so deep
in our tradition, as both so necessary to us and so inade-
quate.

More than one great revolution had ended and had been
almost forgotten as the seventeenth century drew its pic-
ture of the physical world. A centuries-long struggle to
decide whether it were rest or uniform motion that was the
normal state of an undisturbed body no longer troubled
men’s minds: the great clarity, so foreign to everyday ex-
perience, that motion, as long as it was uniform, needed
no cause and no explaining was Newton’s first law. The
less deep but far more turbulent Copernican revolution

NEWTON: THE PATH OF LIGHT 11

was history: the earth revolved about the sun. The physi-
cal world was matter in motion: the motion was to be un-
derstood in terms of the impetus or momentum of the
bodies which would change only for cause, and of the
force that was acting upon it to cause that change. This
force was immediate and proximate. It produced a tend-
ency for the impetus to change, and every course could be
analyzed in terms of the forces deviating bodies from their
uniform motions. The physical world was a world of dif-
ferential law, a world connecting forces and motions at
one point and at one instant with those at an infinitely near
point in space and point of time; so that the whole course
of the physical world could be broken down into finer and
finer instants, and in each the cause of change assigned by
a knowledge of forces.

Of these forces themselves the greatest in cosmic affairs
—that which governed the planets in the heavens and the
fall of projectiles on earth—had been found by Newton
in the general law of gravity. Was this, too, something that
spread from place to place, that was affected only instant
by instant, point by point; or was it a property given as a
whole, an interaction somehow ordained to exist between
bodies remote from one another? Newton was never to
answer this question; but he, and even more than he, Huy-
gens, studying the propagation of light, were laying the
foundations for a definite view—a view in which the void
of the atomists would lose much of its emptiness and take
on properties from the bodies which inhabited it, which in
turn would affect bodies far away.

12 SCIENCE AND THE COMMON UNDERSTANDING

It was not until the nineteenth century and Faraday that
the full richness of space began to be understood: how it
could be the seat not only of gravitational forces produced
by the mass of material particles but of electric and mag-
netic forces produced by their charges. Even in Newton’s
day it was clear that there were very strong forces at work
in lending to material objects their solidity. Newton
wrote:

It seems probable to me, that God in the Beginning
form’d Matter in solid, massy, hard, impenetrable, move-
able Particles, of such Sizes and Figures, and with such
other Properties and in such Proportion to Space, as most
conduced to the End for which he formed them; and that
these primitive Particles being Solids, are incomparably
harder than any porous Bodies compounded of them; even
so very hard, as never to wear or break in pieces; no ordi-
nary Power being able to divide what God himself made
one in the first Creation.

Newton saw that what held atoms together and made mat-
ter must be forces of inordinate strength, and he never con-
sidered their existence without a sense of mystery and
awe. He did not know, nor do we today know, in what
subtle way these forces might or might not be related to
the forces of gravity.

But for many of his contemporaries and successors
these questions appeared less pressing than the confidence
that, once given the forces, the course of nature could be

NEWTON: THE PATH OF LIGHT 13

foretold and that, where the laws of gravity could be
found, other forces would yield to observation and analy-
sis. It is only in this century that we have begun to come
to grips with other instances of antinomy, the apparent
irreconcilability between the differential description of
nature, point by point, instant to instant, and the total
unique law and event. It is only in this century that we
have had to recognize how unexpected and unfamiliar that
relation between bodies and the atoms on the one hand,
and that space full of light and electricity and gravita-
tional forces on the other, could prove to be.

For the eighteenth century the world was a giant
mechanism. It was a causal world, whether or not gravity
and the other forces acting on bodies inhered in them by
their nature or by God’s will or that they, too, grew,
through laws as rigorous as the laws of motion, from the
properties induced in space by the bodies in it. All that
happened had its full, complete, immediate, efficient
cause. The great machine had a determinate course. A
knowledge of its present and therefore its future for all
time was, in principle, man’s to obtain, and perhaps in
practice as well. These objects with which the world was
filled—the heavenly bodies, the impenetrable atoms and
all things composed of them—were found by observation
and by experiment; but it would have occurred to no one
that their existence and their properties could be qualified
or affected by the observations that told of them. The giant
machine was not only causal and determinate; it was ob-

14 SCIENCE AND THE COMMON UNDERSTANDING

jective in the sense that no human act or intervention
qualified its behavior.

A physical world so pictured could not but sharpen the
great gulf between the object and the idea. It would do
much to bring about that long, critical, and, in its later
phase, irrational and mystical, view of the relations be-
tween the knower and the known that started with Locke
and is perhaps even today not fully or happily ended.

It is, of course, clear that many developments in sci-
ence that were to flower in the eighteenth and nineteenth
centuries would soon moderate and complicate the harsh
basic picture of the giant machine and of the vast gulf be-
tween it and the knowing human mind that thought about
it and analyzed its properties. This is true of the great de-
velopment of statistics, which in the end made room for
human ignorance as an explicit factor in estimating the be-
havior of physical forces. It is true of chemistry, whose
phenomena, whatever their ultimate description, looked so
very little like the result of matter in motion. It is even
more true of the biological sciences, where matter in mo-
tion, ever evident and inevitable, appears both at first
sight and upon deeper analysis only marginally relevant
to what makes biological forms interesting.

But with all of this, and with varying degrees of agree-
ment and reservation, there was the belief that in the end
all nature would be reduced to physics, to the giant ma-
chine. Despite all the richness of what men have learned
about the world of nature, of matter and of space, of
change and of life, we carry with us today an image of the

NEWTON: THE PATH OF LIGHT 15

giant machine as a sign of what the objective world is
really like.

This view of the Newtonian world is oversimplified;
perhaps any view of what men made of their new sciences,
their new powers, and their new hopes will be simplified
to the point of distortion. Science for the eighteenth cen-
tury was not a finished undertaking; and, if men were
overwhelmed with what they had learned, they were easily
reminded of how much was still missing. A rational un-
derstanding of the world was not an understanding for one
generation or one man, as it is alleged that it at one time
appeared to be to Descartes. The immense discoveries of
the recent past made it impossible to hold the view that all
that was really worth knowing had long been known—a
view that is a sort of parody, in any case, of the Renais-
sance.

This was a long journey on which men were embarked,
the journey of discovery; they would need their wits and
their resources and their forbearance if they were to get
on with it. But it was a job in which progress was inevita-
ble, and in which the style and success of physical science
would tend to set the style for all undertakings of man’s
reason. What there is of direct borrowing from Newtonian
physics for chemistry, psychology, or politics is mostly
crude and sterile. What there is in eighteenth-century po-
litical and economic theory that derives from Newtonian
methodology is hard for even an earnest reader to find.
The absence of experiment and the inapplicability of New-
tonian methods of mathematical analysis make that inevi-

16 SCIENCE AND THE COMMON UNDERSTANDING

table. These were not what physical science meant to the
enlightenment.

It meant a style of thought, a habit of success, and an
understanding of community quite typical for the age.
These are to be found best in the learned communities that
grew up in Europe and later in America—in the Royal
Society and in the far more ambitious, far more revolu-
tionary, far more programmatic French Academy. These
communities were infused by a confidence in the power
of reason and by a sense of improvement constant and al-
most inevitable in the condition of man’s knowledge, and
therefore of his actions and his life. They rest on a con-
sensus of men, often seeing with their own eyes the crucial
experiment that was to test or to confirm a theory; on the
common experience of criticism and analysis; on the wide-
spread use of mathematical methods with all the assurance
of objectivity and precision that they give us. These were
communities banded together for the promotion of knowl-
edge—critical, rapacious to correct error, yet tolerant
from knowing that error is an inevitable step in acquiring
new knowledge. These were communities proud of their
broad, non-sectarian, international membership, proud of
their styleand their wit, and with a wonderful sense of new
freedom. One may recapture some sense of these com-
munities from the writings of the time. The first history of
the Royal Society is not truly a history but an apology,
written when the society was only a few years old, explain-
ing it, defending it against its critics. Bishop Sprat has
this to say:

NEWTON: THE PATH OF LIGHT 17

Their Purpose is, in short, to make faithful Records of
all the Works of Nature, or Art, which can come within their
Reach; that so the present Age, and Posterity, may be able
to put a Mark on the Errors, which have been strengthened
by long Prescription; to restore the Truths, that have lain
neglected; to push on those, which are already known, to
more various Uses; and to make the way more passable, to
what remains unreveal’d. This is the Compass of their
Design...

They have tried to put it into a Condition of perpetual
Increasing, by settling an inviolable Correspondence be-
tween the Hand and the Brain. They have studied, to make
it not only an Enterprise of one Season, or of some lucky
Opportunity; but a Business of Time; a steady, a lasting, a
popular, an uninterrupted Work . . .

It is to be noted, that they have freely admitted Men of
different Religions, Countries, and Professions of Life.
This they were oblig’d to do, or else they would come far
short of the Largeness of their own Declarations. For they
openly profess, not to lay the Foundation of an English,
Scotch, Irish, Popish, or Protestant Philosophy; but a
Philosophy of Mankind.

Reading this today, we can hardly escape a haunting
sense of its timeliness and a certain nostalgia at how little
the texture of our life conforms to these agreeable and
noble ideals. We cannot perhaps wholly forget how much
these communities owed to the long centuries of Christian
life and Christian tradition; how much that they then took
for granted in their inquiries and thoughts, in their whole

18 SCIENCE AND THE COMMON UNDERSTANDING

style, derived from a way of life and a history which they
were about to change beyond all recognition; and how
deeply this, their program, could alter the very men and
the very minds to whom their program would in time be-
come entrusted.

These, however, were not reflections to darken much the
eighteenth century or to cast real shadows on that great
path of light, that renewed hope of men for a growing and
growingly rational comprehension of their world and of
themselves. At the very end of the century in another land
largely nourished and fathered by the enlightenment, a
gentleman and patriot wrote a letter. He wrote in answer
to a young friend inquiring about his present course of
study. He wrote in the last days of the Directorate, when
the course of history was diverging in alarming and im-
mense ways from that charted by the men of the French
Academy. He wrote it about two years before he was to
assume the Presidency of the United States, there for over
a century to raise more firmly than ever before the stand-
ard of man’s freedom, his progress, and his rational na-
ture.

I am among those who think well of the human char-
acter generally. I consider man as formed for society, and
endowed by nature with those dispositions which fit him
for society. I believe also, with Condorcet, as mentioned in
your letter, that his mind is perfectible to a degree of which
we cannot as yet form any conception . . . science can
never be retrograde; what is once acquired of real knowl-
edge can never be lost. To preserve the freedom of the

NEWTON: THE PATH OF LIGHT 19

human mind then and freedom of the press, every spirit
should be ready to devote himself to martyrdom; for as
long as we may think as we will, and speak as we think, the
condition of man will proceed in improvement. The gen-
eration which is going off the stage has deserved well of
mankind for the struggles it has made, and for having ar-
rested that course of despotism which had overwhelmed
the world for thousands and thousands of years. If there
seems to be danger that the ground they have gained will
be lost again, that danger comes from the generation your
contemporary. But that the enthusiasm which characterises
youth should lift its parracide hands against freedom and
science would be such a monstrous phaenomenon as I can-
not place among possible things in this age and country.

The writer of the letter was Thomas Jefferson.

SCIENCE AS ACTION:

RUTHERFORD’S WORLD

IT IS inherent in the very notion of culture and of
tradition that there is a cumulative aspect to human life.
The past underlies the present, qualifies and moderates it,
in some ways limits it and in some ways enriches it. We
understand Shakespeare better for having read Chaucer,
and Milton for having read Shakespeare. We appreciate
Trevelyan more for knowing Thucydides. We see Cézanne
with better eyes for having looked also at Vermeer, and
understand much more in Locke for knowing Aristotle, St.
Matthew for knowing Job. But in actual fact we rather
seldom bring a knowledge of the earlier to our first ac-
quaintance with the later; and if it is true that Job throws
light on Matthew, it is also true that Matthew throws light
on Job. We can understand a great deal of what is written
today, knowing little explicitly of what has been written
in the past. We can and do know a great deal of what
Shakespeare means and intends without any knowledge

SCIENCE AS ACTION: RUTHERFORD’S WORLD 21

of those earlier men who altered and educated his sensi-
bility.

The cumulative character of science is very different
and very much more essential. It is one of the reasons for
the great difficulty of understanding any science in which
one has not largely become an expert—the science of
which Hobbes wrote: “Of that nature, as none can under-
stand it to be, but such as in good measure have attayned
it.”

There are at least two reasons for this: one has to do
with the relation of later discoveries in science to earlier,
and the other with the use that is made of earlier work in
science as an instrument of progress. When we find out
something new about the natural world this does not super-
sede what we knew before; it transcends it, and the tran-
scendence takes place because we are in a new domain of
experience, often made accessible only by the full use of
prior knowledge. The work of Huygens and Fresnel on the
wave properties of light is as necessary today as it ever
was, although we know that there are properties of light
which are left out in their account and their experience,
properties which, in the context of atomic happenings, are
decisive. Newton’s law of gravitation and his equations of
motion apply to and underlie immense realms of physical
experience and are not made wrong by the fact that in
other and still vaster spheres they must be replaced by the
broader laws of Einstein. The chemical theory of valency
has been explained, elucidated, and, to some small degree,
extended by an understanding, in terms of the behavior of

22 SCIENCE AND THE COMMON UNDERSTANDING

electrons and nuclei, of what goes on in chemical bonding;
but the chemical theory of valency is not superseded and
will presumably be used as long as man’s interest in
chemistry continues. The foundations of solid fact and the
laws which describe it persevere through the whole course
of science, to be refined and adapted to new contexts but
never to be ignored or cast out.

But this is only a part of the story. It is a recurring ex-
perience of scientific progress that what was yesterday an
object of study, of interest in its own right, becomes today
something to be taken for granted, something understood
and reliable, something known and familiar—a tool for
further research and discovery. Sometimes the new instru-
ment which is used to extend experience is a natural phe-
nomenon, only barely qualified or controlled by the ex-
perimenter. We are familiar with the use of calcite crys-
tals to produce two separate beams of polarized light. We
know that the cosmic rays are both an object of investiga-
tion in themselves and a tool of hitherto unparalleled
power for probing the properties and transmutations of
primordia] matter here on earth and in the laboratory.
Sometimes past knowledge is embodied not in a natural
phenomenon but in an invention, or in elaborate pyramids
of invention, a new technology.

There are many well known and major examples of
technological development during the last war which have
added to the instruments of the investigator of the physical
and biological world. We may recall two. Microwave
radar—the generation, control, and detection of elec-

SCIENCE AS ACTION: RUTHERFORD’S WORLD 23

tromagnetic waves of relatively very short length—played
a heroic part in the Battle of Britain. In the years since,
it has provided powerful new means of investigating
atomic, molecular, and even nuclear problems from which
in actual fact subtle discoveries have been made about the
laws of interaction of electrons and protons and neutrons.

The nuclear reactor embodies in its technology very re-
cently acquired understanding of the fission processes in
uranium and of the behavior of neutrons in their collisions
with atomic nuclei; it is now an important tool whose con-
trolled and well-understood radiations are telling us about
properties of matter hitherto barely accessible. Artificially
radioactive substances made in great profusion by atomic
reactors enable us to follow the course of individual atoms
in chemical and biological changes. In biology especially
they may be an addition to our instrumental facilities and
techniques comparable in importance with the microscope
itself.

It is an oversimplification to say that technologies based
upon recently discovered natural phenomena are taken as
wholly for granted and as wholly known, but this is es-
sentially the truth. They are added to the experimenter as
a good tool is added to the artisan; as the pencil in the
writer’s hand ceases to be an object in itself and becomes
almost a part of the writer; or as a horse under a good
horseman becomes for the time being not an animal to be
cared for and thought about but a part of the entity “‘horse-

24 SCIENCE AND THE COMMON UNDERSTANDING

man.” Thus what has been learned and invented in science
becomes an addition to the scientist, a new mode of per-
ception, a new mode of his action.

There are some cautions to be added to this. No experi-
menter takes his equipment quite so much for granted that
he fails to check whether in fact it is performing as it is
supposed to perform; but the notion of how it is supposed
to perform is for him in general a fixed thing not calling
for further inquiry. This may be true even when the in-
vention is a sample of practical art rather than a sample
of true understanding. The photographic plate has served
as an instrument of science for decades, during which its
behavior was only very incompletely understood. Any
machine can get out of order, and in a laboratory most ma-
chines do. The horse is shod and bridled and fed before he
can become part of the horseman. Nevertheless we use
what we have learned to go further. A perpetual doubting
and a perpetual questioning of the truth of what we have
learned is not the temper of science. If Einstein was led to
ask not ‘‘What is a clock?” but “How, over great dis-
tances and with great precision, do we synchronize
clocks?” that is not an illustration of the scepticism of
science; it exemplifies rather the critical reason creating
a new synthesis from paradoxes, anomalies, and bewilder-
ments, which experiments carried on with new precision
and in a new context brought into being.

All this means that science is cumulative in a quite spe-
cial sense. We cannot really know what a contemporary
experiment means unless we understand what the instru-

SCIENCE AS ACTION: RUTHERFORD’S WORLD 25

ments and the knowledge are that are involved in its de-
sign. This is one reason why the growing edge of science
seems so inaccessible to common experience. Its findings
are defined in terms of objects and laws and ideas which
were the science of its predecessors. This is why the stu-
dent spends many long years learning the facts and arts
which, in the acts of science, he will use and take for
granted—why this long tunnel, at the end of which is the
light of discovery, is so discouraging for the layman to
enter, be he an artist, scholar, or man of affairs.

This conversion of an object of study into an instrument
has its classic exemplification in Rutherford and the a-
particle. This is a trail we will follow for some time. It
will lead us to the heart of atomic physics. The a-particle,
emitted by many naturally radioactive substances, identi-
cal with the nucleus of helium, was indeed a strong right
arm for Rutherford and all his school in probing the
atomic world. Rutherford’s early works had been largely
devoted to writing the wonderful natural history of the
radioactive families—those which start with spontaneous
changes in the heavy elements uranium and thorium. Part
of the natural history was to discover the genetic relations
between the various radioactive substances, some of them
growing as a result of the decay of others and in turn giv-
ing rise to daughter products by further transmutation.

The natural history involves a chemical identification
of the radioactive substances, the determination of the
rapidity of their decay and of the alternative modes of
decay, which some of them exhibit. It involves the recogni-

26 SCIENCE AND THE COMMON UNDERSTANDING

tion of three fundamentally different kinds of radiation,
all of which appear at one stage or another in these family
histories. This identification, which we shall meet again in
later contexts, means learning some of the basic properties
of the particles emitted. This identification, as we shall
shortly see, is made possible by the fact that even a single
such particle has readily detectable effects.

These properties include the mass of the particle and its
electric charge. These have usually been found in the first
instance by studying their behavior in large-scale electric
and magnetic fields and applying Newton’s laws to
analyze their motion. These same methods give one a
measure of the velocity or energy with which the particles
are emitted, and of the loss of this energy as the particles
pass through matter. Sometimes, at a later stage, the prod-
ucts of an atomic or nuclear disintegration can be more
thoroughly studied. They may have more subtle electro-
magnetic properties than charge, such as a small magnetic
moment. They may have structure or size. But the basic
identifications can all be made in terms of the response
of the radiations to familiar, large-scale, experimentally
controllable situations like the classical electric and mag-
netic fields of our laboratory courses.

The a-particle of the naturally radioactive substances
became for the middle years of Rutherford’s life the
sharpest experimental tool; it was to be supplemented and
to some extent superseded only when artificially accel-
erated nuclei became available during the nineteen-thir-
ties. The essential features of the experiments that have

SCIENCE AS ACTION: RUTHERFORD’S WORLD 27

told us most about atoms and nuclei and the ingredients of
matter are two: one has to do with structure, and the other
with scale.

The structure of the experiment involves three parts: a
probe, which is an object meant to explore or disturb mat-
ter in its natural state, typically with some degree of vio-
lence. This was the role of the a-particle. The second ele-
ment is the target, which is some form of matter, whether
pure or of controllable and manageable complications;
and the third is the detector, which identifies and describes
the objects emerging from the disturbance, whether they
be the altered or the unaltered probe, or something
knocked out of the target, or created in the collision, or
something appearing long after the collision as evidence
of a rearrangement of the collision products consequent
upon the disturbance. This is not a universal pattern—this
probe-target-detector assembly. The collision is not the
only way of learning about atomic systems; but almost all
of what we have learned has derived at least in part from
such experiments and can be elucidated in terms of them.

As to scale, it is the scale that determines the possibility
of detection. The events that are so studied—the colli-
sions, transmutations—can typically be studied event by
event, atom by atom. The reason for this lies in two cir-
cumstances: one is that in nuclear transformations, and
even more so in transformations induced by cosmic rays
and superaccelerators, the energy characteristic of a sin-
gle atomic process is enormous compared to the chemical
energies, and is sufficient to produce recognizable physical

28 SCIENCE AND THE COMMON UNDERSTANDING

and chemical changes in hundreds of thousands or even
millions of atoms.

The second circumstance lies in the art that has been de-
voted toward exploiting these energies in systems of detec-
tion. The detectors for Rutherford’s experiments are by
now familiar. One is the scintillation screen, where an a-
particle creates a flash of light easily visible through a
microscope at the point where it hits the screen. Another is
the beautiful cloud chamber of C. T. R. Wilson, which is,
according to legend, an outcome of the inventor’s interest
in the mist and clouds and rain of his native Scotland. In
this cloud chamber the track of a charged particle is
marked by the occurrence of innumerable small yet
readily visible droplets of water or other liquid close to
where the particles passed. A third is the counter, in which
the electrical disturbance produced in a gas by the passage
of a charged particle gives rise to a substantial electrical
discharge, which can be amplified and analyzed by elec-
tronic circuitry.

These detectors have been supplemented by many,
many others; and the precision and power of electronic
amplification and analysis have been developed into a
great art. The detector of atomic physics still characteristi-
cally is designed to take advantage of the very great en-
ergy involved in the changes of a single atom, and of the
power to amplify this energy almost at will to make it ac-
cessible. The clicking counters and flashing lights and oc-
casionally even the ringing bells of a modern nuclear labo-
ratory make the doings of individual atoms very vivid and

SCIENCE AS ACTION: RUTHERFORD’S WORLD 29

immediate, and make the subtle atoms of Epicurus or of

Newton seem very private and remote.

Rutherford and his probing a-particles and detectors
are old history, dating back roughly some forty years.
They are basic alike to atomic and nuclear physics, basic
as a foundation for the great revolution in science which it
is my principal purpose to describe, and for the further
developments at the very forefront of contemporary dis-
covery that have us:today perplexed and bemused. With
his a-particles, obtained from natural radioactivity, Ruth-
erford discovered the atomic nucleus and the nuclear
model of the atom; with some help from other evidence he
discovered the mass and the charge of the various atomic
nuclei and thus rationalized Mendelyeev’s table of the ele-
ments. With the a-particles, he was able to touch nuclear
matter itself and measure its dimensions. He showed that
it could be transmuted; he identified at least some of its
ingredients.

For the most part, a-particles when they pass through a
bit of matter are not very much deflected or changed in di-
rection; they are gradually slowed down; but occasionally
a particle will change its direction of motion very greatly.
It will be scattered through a large angle; it will act as
though some great force had disturbed it, as though it had
hit something quite small and quite hard. The law describ-
ing these deflections is Rutherford’s law; and to it he gave
a simple meaning: there are forces acting on the a-parti-

30 SCIENCE AND THE COMMON UNDERSTANDING

cles; they are not unfamiliar to physics. They are the elec-
tric repulsion between the charge of the atomic nucleus
and the charge of the a-particle—the same force which
manifests itself when two positively charged pith balls
push each other apart in an elementary demonstration.
The balls repel each other because the two charges are
similar; and the repulsion is described by Coulomb’s law
—very much the same law as Newton’s law of gravitation.
The repulsion is inversely proportional to the square of
the separation of the charges. The charge of the atomic
nucleus is a multiple of that of the proton—the nucleus of
hydrogen. The multiple is the atomic number, which de-
termines the number of electrons in the atom, and almost
all the chemical properties of the element, and the position
in the periodic table of that element. The mass of the
nucleus is almost the whole mass of the atom as expressed
by its atomic weight. This charge and mass is concentrated
in a small volume. Everywhere outside it, the a-particle
feels only the electric field.

By using a-particles fast enough to overcome the elec-
tric repulsion, and using light elements for which the
charge and therefore the repulsion are not too great, Ruth-
erford found that occasionally a-particles penetrated to a
different domain entirely, where very strong forces, not
electric forces, deflected them. In this way he found the
dimensions of the nucleus itself: roughly one part in 10,-
000 of the dimensions of the atom as a whole. This char-
acterized the nucleus as a region of incredibly high den-
sity, of many millions of tons per cubic inch. Rutherford

SCIENCE AS ACTION: RUTHERFORD’S WORLD 31

discovered even more: he was able to show that when fast
a-particles penetrated nuclear matter things other than a-
particles emerged from the mélée. In experiments under-
taken during the First World War, and justified by Ruther-
ford as of greater importance than any contribution he
could then make to the prosecution of that war, Rutherford
for the first time induced by human action the transmuta-
tion of an atomic nucleus, knocking out of the nucleus of
nitrogen a nucleus of hydrogen, or proton, and starting a
chain of events which led, among many things, to man’s
release of atomic energy, to what may some day be judged
the most compelling argument of all for putting an end to

war itself.

The story went on from there. Before we revert to the
nuclear model of the atom and how oddly different its
properties are from any we can understand on the basis of
Newtonian physics, we may follow sketchily and partially
this course of discovery with probe, target, and detector
that Rutherford initiated and that has continued until the
present day. Twenty years ago, using the same a-particles
as probes, Chadwick managed to identify another survivor
of the disturbance, another ingredient of the nucleus, the
neutron, which has roughly the proton’s mass but no
charge, and thus to lay the foundations for an elementary
view of nuclear composition. The nucleus is made up of
neutrons and protons—enough protons to account for its
charge, the atomic number; enough neutrons to account

32 SCIENCE AND THE COMMON UNDERSTANDING

for the excess of its atomic weight over its atomic number
—held together in their tiny volume by strong forces
wholly dissimilar from those of electricity and magnetism,
whose description even today is a far from completely
solved problem.

Chadwick’s neutrons, in their turn, became probes, in-
ducing nuclear transmutations very copiously, because
they were not kept away from nuclei by the positive nu-
clear charge. Their use led, in the years just before the
war, to Hahn’s discovery that, when uranium was trans-
muted by being hit by neutrons, among the products was
barium, a large half of the original nucleus, but only
about half—and thus to nuclear fission.

Even this was only the beginning. In the very energetic
particles of cosmic radiation, in the nuclei accelerated by
giant modern accelerators to energies a hundredfold those
of Rutherford’s a-particles, we have found new probes to
elicit new phenomena; the story of sub-nuclear matter be-
gan to unfold and ramify. A whole new family of hitherto
unknown, and, for the most part, unrecognized and unex-
pected objects began to emerge from the nuclear encoun-
ters. The first of these were the various mesons, some
charged and some uncharged, about ten times lighter than
the proton and some hundreds of times heavier than the
electron. In the last years there have appeared in increas-
ing variety objects heavier than the mesons, other objects
heavier even than protons, whose names are still being
changed, from month to month, by solemn conferences.
Physicists call them vaguely, and rather helplessly, “the

SCIENCE AS ACTION: RUTHERFORD’S WORLD 33

new particles.” They are without exception unstable, as in
the neutron. They disintegrate after a time which varies
from one millionth to less than a billionth of a second into
other lighter components. Some of these components are
in turn unfamiliar to physics and are themselves in turn
unstable. We do not know how to give a clear meaning to
this question. We do not know why they have the mass and
charge that they do; why they and just they exist; why they
disintegrate as they do; why in most cases they last as long
as they do, or anything much about them. They are the
greatest puzzle in today’s physics. '

But all this is now; and these were not the puzzles of
Rutherford’s day. To these we shall turn in the next lec-
tures. They become manifest when we try to deduce and
describe the properties of Rutherford’s atom in terms of
Newtonian mechanics. This attempted description failed.
The atoms of nature are radically, dramatically, unlike
atoms, composed as Rutherford found of electrons and
small nuclei, subject to the forces Rutherford discovered
and described, and moving according to Newton’s laws.
The failure of this classical description turned out to be a
major clue, one of the few major clues, in the atomic story.
We learned, before the story was finished, that more than
Newtonian mechanics would have to be modified if we
were to understand and describe our experience with
atomic systems. We would have to alter our ideas on very
fundamental points, on causality, for instance, and even
on the nature of the objectivity of parts of the physical
world. We were to be reminded, in a quite unexpected

34 SCIENCE AND THE COMMON UNDERSTANDING

way, of the nature and limitations, as well as the power,
of human knowledge itself. It is largely for this reason
that the story of atomic discovery has appeared to me so
full of instruction for us all, for layman as well as special-
ist. For it has recalled to us traits of old wisdom that we
can well take to heart in human affairs.

Before these great changes could be completed, and the
strange situation elucidated, many new ideas and methods
of description were to be introduced. We learned words
new for us, like “quantum,” and “‘state,”’ words like “‘cor-
respondence” and “complementarity,” words with a new
meaning for physics. Of these the word “‘correspondence”
came to stand for the conservative and traditional traits of
the new physics, that bound it to the physics of the past;
whereas “complementarity” described, as we shall come
to see, those new features, unknown to the physics of New-
ton, that have broadened and humanized our whole under-
standing of the natural world.

Time and experience have clarified, refined, and en-
riched our understanding of these notions. Physics has
changed since then. It will change even more. But what we
have learned so far, we have learned well. If it is radical
and unfamiliar and a lesson that we are not likely to for-
get, we think that the future will be only more radical and
not less, only more strange and not more familiar, and that
it will have its own new insights for the inquiring human
spirit.

A SCIENCE IN CHANGE

OUR understanding of atomic physics, of what we
call the quantum theory of atomic systems, had its origins
at the turn of the century and its great synthesis and reso-
lutions in the nineteen-twenties. It was a heroic time. It
was not the doing of any one man; it involved the collabo-
ration of scores of scientists from many different lands,
though from first to last the deeply creative and subtle and
critical spirit of Niels Bohr guided, restrained, deepened,
and finally transmuted the enterprise. It was a period of
patient work in the laboratory, of crucial experiments and
daring action, of many false starts and many untenable
conjectures. It was a time of earnest correspondence and
hurried conferences, of debate, criticism, and brilliant
mathematical improvisation.

For those who participated, it was a time of creation;
there was terror as well as exaltation in their new insight.
It will probably not be recorded very completely as his-

36 SCIENCE AND THE COMMON UNDERSTANDING

tory. As history, its re-creation would call for an art as
high as the story of Oedipus or the story of Cromwell, yet
in a realm of action so remote from our common experi-
ence that it is unlikely to be known to any poet or any his-
torian. In other ways, there will be such times again. Most
of us are convinced that today, in our present probings in
the sub-atomic and sub-nuclear world, we are laying the
groundwork for another such time for us and for our sons.
The great growth of physics, the vast and increasingly com-
plicated laboratories of the mid-twentieth century, the in-
creasing sophistication of mathematical analysis, have al-
tered many of the conditions of this new period of crisis.
We do not think that they will have altered its heroic and
creative character.

When quantum theory was first taught in the universi-
ties and institutes, it was taught by those who had partici-
pated, or had been engaged spectators, in its discovery.
Some of the excitement and wonder of the discoverer was
in their teaching; now, after two or three decades, it is
taught not by the creators but by those who have learned
from others who have learned from those creators. It is
taught not as history, not as a great adventure in human
understanding, but as a piece of knowledge, as a set of
techniques, as a scientific discipline to be used by the
student in understanding and exploring new phenomena
in the vast work of the advance of science, or its applica-
tion to invention and to practical ends. It has become not
a subject of curiosity and an object of study but an in-
strument of the scientist to be taken for granted by him,

A SCIENCE IN CHANGE 37

to be used by him, to be taught to him as a mode of
action, as we teach our children to spell and to add.
What we must attempt to do in these talks is wholly dif-
ferent. This is no school to learn the arts of atomic physics.
Even those prior arts—the experimental tools, the mathe-
matical powers, the theories, inventions, instruments, and
techniques which defined the problems of atomic physics,
which established the paradoxes, described the phenom-
ena, and underlay the need for synthesis—are not known
to us of our own experience. We must talk of our subject
not as a community of specialized scientists but as men
concerned with understanding, through analogy, descrip-
tion, and an act of confidence and trust, what other people
have done and thought and found. So men listen to ac-
counts of soldiers returning from a campaign of unparal-
leled hardship and heroism, or of explorers from the high
Himalayas, or of tales of deep illness, or of a mystic’s
communion with his God. Such stories tell little of what
the teller has to tell. They are the threads which bind us in
community and make us more than separate men.

Here, then, we have our atoms. Their ingredients have
been made manifest by Rutherford and his a-particles, as
have the forces that act between the ingredients, and by
probing with electrons and with light as well as with a-par-
ticles. There is the nucleus, with almost the whole of the
atom’s mass and almost none of its size, and with a charge
which is measured by the atomic number, equal to the

38 SCIENCE AND THE COMMON UNDERSTANDING

number of electrons that surround the nucleus in the nor-
mal atom. We have the simple laws of attraction and re-
pulsion, familiar from the large-scale, everyday experi-
ence with electricity. Unlike charges attract and like repel;
and the forces, like Newton’s, decrease inversely with the
square of their separation.

In Rutherford’s day it seemed reasonable, as it no
longer entirely does today in facing our modern physics,
to subdivide the problem of atomic structure into three
questions: what are the ingredients of the atom; what are
the forces, and the laws of force, acting between these in-
gredients; how in response to those forces do the ingredi-
ents move? We know that even in atomic problems this
division is not completely rigorous; but the refinements are
minor and have largely proved tractable. They consist of
taking into account the effect of the motion of the particles
themselves on the forces between them and, in some cases,
the distortion of the properties of particles, very small it-
self in the atomic structures, by the presence of other par-
ticles and the forces that they exert. It is surely not wholly
true of the nucleus that these distortions are small; and in
the strange objects which emerge so readily when nuclei
undergo violent collisions we have persuasive, if indirect,
evidence for that.

The atom, then, has a massive charged nucleus; the
atom as a whole is neutral and 10,000 to 100,000 times as
far across as its tiny nuclear core. The rest of the atom is
composed of electrons and electric fields—electrons that
are the universal ingredients of matter, the determinants

A SCIENCE IN CHANGE 39

of almost all its chemical properties and of most of its
familiar physical properties as well. There will be as many
electrons in the atom as the atomic number, the nuclear
charge; this makes the atom as a whole neutral. There will
be one electron in hydrogen and thirteen in aluminum and
ninety-two in uranium. These are the ingredients; and the
laws of force, complex only in the last refinements, are
basically simple. The electron feels an attractive Coulomb
force exerted by the nucleus, attractive since the electron
and nucleus are oppositely charged, and once again fall-
ing off with distance in the same way as gravitational
forces according to Newton’s law. For hydrogen, this
means a simple situation: two bodies with a force between
them identical in structure with that which the sun exerts
on the planets; two bodies small enough compared to the
atom’s size so that they almost never touch, and the prop-
erties of their contact can have little influence. The law of
forces has been verified not only by probing with particles,
by which it was originally discovered, but by probing with
electrons themselves, in the first instances by the beta rays
of naturally radioactive substances. For other atoms there
is in addition the electrical repulsion between the several
electrons, balancing to some extent the nuclear attraction.
And there is, further, the well-known mathematical com-
plication of describing quantitatively the behavior of a
system with many particles.

But with hydrogen this should not be so. Here we have
essentially a single light body moving in a simple and well-
known force. The description of this system should be a

40 SCIENCE AND THE COMMON UNDERSTANDING

perfect example of Newtonian dynamics, and should, in
its refinements, be intelligible in terms of all that the nine-
teenth century had discovered about the behavior of
charged particles in motion and the electromagnetic radia-
tion produced when they are accelerated.

But it did not turn out that way. To what appeared to
be the simplest questions, we will tend to give either no
answer or an answer which will at first sight be reminiscent
more of a strange catechism than of the straightforward
afirmatives of physical science. If we ask, for instance,
whether the position of the electron remains the same, we
must say “no”; if we ask whether the electron’s position
changes with time, we must say “no”; if we ask whether
the electron is at rest, we must say “no”; if we ask whether
it is in motion, we must say “no.” The Buddha has given
such answers when interrogated as to the conditions of a
man’s self after his death; but they are not familiar an-
swers for the tradition of seventeenth- and eighteenth-cen-
tury science.

Let us review, then, what a hydrogen atom should be
like if we could apply Newton’s laws and the whole clas-
sical picture of matter in motion to the simple model. The
electron is held to its nucleus as the earth is to the sun, or
as is Venus. It should revolve in an ellipse, as Kepler
found and Newton explained. The size of the ellipse could
be varied from atom to atom as the orbits of the planets
are different, depending on how it was formed and what

A SCIENCE IN CHANGE 41

its history, and so should the shape of the orbits, whether
they are narrow or round. There should be no fixed size
for a hydrogen atom and no fixed properties; and when we
disturb one by one of our probings, or when it is disturbed
in nature, we would not expect it to return to a size and
shape at all similar to that from which it started. This is
not all—there are more recondite points. When a charge
moves in anything but a straight line, it should send out
electromagnetic radiation. This is what we see in every
radio antenna. As far as our model goes, this radiation
should in time sap the energy of the electron to make up
for the energy that has been sent out in the form of light
waves; and the ellipses on which the electron moves should
get smaller and smaller as it gets nearer to its attractive
sun and loses its energy. For a system about the size of the
hydrogen atom as we know it in nature, a few hundredths
of a millionth of an inch across, this process should go
very rapidly; and the atom should become far, far smaller
than atomic dimensions in very much less than a millionth
of a second. The color of the light that the electron radiates
should be determined by the period of its revolution; it too
should be random, differing from orbit to orbit, differing
from time to time as the orbits shrink and alter. This is the
picture which classical physics—Newtonian physics—pre-
dicts for the hydrogen atom, if Rutherford’s model is right.

It could hardly be further from the truth. By all we
know, hydrogen atoms if undisturbed are all identical.
They are the same size and each has the same properties
as any other, whatever its history, provided only that it has

42 SCIENCE AND THE COMMON UNDERSTANDING

had achance to recover from any disturbance. They last in-
definitely. We think of them, rightly, as completely stable
and unchanging. When they are undisturbed, they do
not radiate light or any other electromagnetic radiation, as
indeed they could not if they are to remain unaltered.
When they are disturbed, they sometimes do radiate, but
the color of the light that they emit is not random and con-
tinuous but falls in the sharp lines of the hydrogen spec-
trum. The very stability, extent, and definiteness is not at
all understandable on the basis of classical physics; and
indeed on the basis of classical physics there is no length
that we can define in terms of the masses and charges of
the ingredients of the atom, and that is even roughly of
the actual dimensions of the atom.

In other respects, too, the atomic system shows a pe-
culiar lack of continuity wholly at variance with the prop-
erties of Newtonian dynamics. If we probe atoms with a
stream of electrons, for instance, the electrons will typi-
cally lose some of their initial energy, but these losses are
not random in amount. They correspond to definite, well-
defined energy gaps, characteristic for the atom in ques-
tion, reproducible and not too hard to measure. When
an atom is irradiated by light, an electron will be ejected,
if and only if the energy of that light exceeds a certain
minimum knownas the photo-electric threshold. Indeed, it
was this discovery which led Einstein in the early years of
the century to a finding about light almost equally revo-
lutionary for our understanding of light and for our un-
derstanding of atomic systems. This finding, to be more
precise, is that as one alters the frequency of the light that

A SCIENCE IN CHANGE 43

shines on a body, the energy of the electrons ejected in-
creases linearly with the frequency; linearly—that means
proportionally. The constant of proportionality, which
connects energy with frequency, is the new symbol of the
atomic domain. It is called Planck’s constant, or the quan-
tum of action, and it gives a measure of energy in terms
of frequency. It is the heraldic symbol over the gateway
to the new world; and it led Einstein to the bold, though
at the time hardly comprehensible, conclusion that light,
which we know as an electromagnetic disturbance of
rapidly changing. electrical fields, which we know as a
continuous phenomenon propagating from point to point
and from time to time like a wave, is also and is neverthe-
less corpuscular, consisting of packets of energy deter-
mined by the frequency of the light and by Planck’s con-
stant. When a material system absorbs light, it absorbs
such a packet, or quantum, of energy, neither less nor
more; and the discontinuous nature of the energy ex-
changes between an atom and an electron is paralleled by
the discontinuous nature of the energy exchanged when
radiation is absorbed or emitted.

We shall have to come back more than once to light as
waves, and light as quanta; but how radical a problem of
understanding this presents can be seen at once from all
of classical optics, from the work of Huygens and its
mathematical elaboration by Fresnel, and even more com-
pletely from its electromagnetic interpretation by Max-
well. We know that light waves interfere. We know,
that is, that if there are two sources of light, the
intensity of the light to be found at some other place

44 SCIENCE AND THE COMMON UNDERSTANDING

will not necessarily be just composed of the sum of
that which comes from the two sources; it may be more
and it may be less. We know from unnumbered attempts
how to calculate, and how to calculate correctly, what the
interference of the sources will turn out to be. If we have
light impinging on a screen which is opaque and there are
two holes in the screen, not too large and not too far apart
in the terms of the wave length, the wavelets that come
from one of the holes will be added to those that come
from the other. Where two crests of these wavelets coin-
cide, we shall have more light than the sum of the two.
Where a crest and a trough coincide, we shall have less;
and so we observe and understand and predict and are
quite confident of these phenomena of interference.

Try for a moment to describe this in the terms of the
passage of particles of quanta. If one of those quanta
which characterize both the emission of light at the source
and its detection—let us say, by the eye or by the photo-
graphic plate or photo-cell on the far side of the screen—
if a quantum passes through one of the holes, how can the
presence of the other hole through which it did not pass
affect its destiny? How can there be any science or any
prediction if the state of affairs remote from the trajec-
tory of the quantum can determine its behavior? Just this
question and our slow answer to it will start us on the un-
ravelling of the physics of the atomic world.

The first great step, taken long before the crisis of quan-
tum theory, was to find a way of describing atomic behav-

A SCIENCE IN CHANGE 45

ior, not forgetting the mechanics and electrodynamics of
the past, but knowing that one had here to do with some-
thing new and different, and necessarily postponing the
question of the connection of that which is new with the old
laws. This is Bohr’s first theory. It has given us the symbol
of the atomic world: the nucleus and a series of circles and
ellipses represent in a pictorial way the states of the atom.
We use it today, though we know in far more detail and
far more completely what Bohr knew when he proposed it,
that it could be at best a temporary and partial analogy.
This was Bohr’s first postulate: that in every atom there
were stationary states whose stability and uniqueness
could not be understood in terms of classical dynamics.
The lowest one, the one with the least energy, the ground
state, is truly stable. Unless we disturb it, it will last un-
altered. The others are called excited states, and they may
be excited by collision or radiation or other disturbance.
They, too, are stable in a sense incomprehensible in terms
of Newton’s theory. Their stability is not absolute though.
Just as these states could be reached by transition induced
by collision or disturbance, so an atom may return to states
of lower energy, whether by further collision or spon-
taneously. In these spontaneous changes it gives out that
radiation which is the analog of the radiation which in
classical theory would make all motion unstable. In simple
cases, the energy of these stationary states and some of the
properties such as their shape are identical with or similar
to the energy of some of the properties of Newtonian or-
bits. But this stops being true when we go even from hy-

46 SCIENCE AND THE COMMON UNDERSTANDING

drogen to helium, with its two electrons. It is only partially
true in hydrogen; and the rules which Bohr laid down for
determining the character of the orbits that would corre-
spond to stationary states, the so-called quantum condi-
tions, were from the first recognized by him as incomplete
and provisional. We know now that the states are in fact
nothing like orbits at all; that the element of change with
time, which is inherent in an orbit, is missing from these
states; and that in fact the very notion of an orbit can be
applied to the motion of matter only when the stationary
state is not defined, and that a stationary state can exist
only when there is no possibility of describing an orbit at
all.

That was the first rule. And what is the second? The
second rule is that an atom can change only by passing
from state to state; that its energy changes by the differ-
ence in energy between the states; and that, when this ex-
change of energy occurs in the absorption, emission, or
scattering of light, the frequency of the light will be re-
lated to the energy by the relation of Einstein and of
Planck. The energy will be the frequency multiplied by
the quantum of action; thus atomic spectra directly reveal
energy differences between states, and by this the whole
field of spectroscopy becomes evidence for the location
and the properties of atomic states, and we begin to learn
what properties of these states are like those of classical
orbits and what are unlike.

But what are we to think of the transitions themselves?
Do they take place suddenly? Are they very quick mo-

A SCIENCE IN CHANGE 47

tions, executed in going from one orbit to another? Are
they causally determined? Can we say, that is, when an
atom will pass from one of its states to another as we dis-
turb it; and can we find what it is that determines that
time? To all these questions, the answer would turn out
to be “no.” What we learned to ask was what determined
not the moment of the transition but the probability of the
transition. What we needed to understand was not the state
of affairs during the transition but the impossibility of
visualizing the transition—an even more radical impos-
sibility than with the states themselves—in terms of the
motion of matter. We learned to accept, as we later
learned to understand, that the behavior of an atomic
system is not predictable in detail; that of a large number
of atomic systems with the same history, in, let us say, the
same state, statistical prediction was possible as to how
they would act if they were let alone and how they would
respond to intervention; but that nowhere in our battery of
experimental probings would we find one to say what one
individual atom would in fact do. We saw in the very heart
of the physical world an end of that complete causality
which had seemed so inherent a feature of Newtonian

physics.

How could all this be and yet leave the largely familiar
world intact as we knew it? Large bodies are, of course,
made up of atoms. How could causality for bullets and
machines and planets come out of acausal atomic behav-

48 SCIENCE AND THE COMMON UNDERSTANDING

ior? How could trajectories, orbits, velocities, accelera-
tions, and positions re-emerge from this strange talk of
states, transitions, and probabilities? For what was true
yesterday would be true still, and new knowledge could
not make old knowledge false. Is there a possible unity
between the two worlds and what is its nature?

This is the problem of correspondence. Whatever the
laws which determine the behavior of light or of electrons in
atoms or other parts of the atomic world, as we come closer
and closer to the familiar ground of large-scale experience,
these laws must conform more and more closely to those
we know to be true. This is what we call the principle of
correspondence. In its formulation the key is the quantum
of action, whose finiteness characterizes the new features
of atomic physics. And so the physicist says that, where
actions are large compared to the quantum of action, the
classical laws of Newton and Maxwell will hold. What this
tends to mean in practice is that when mass and distances
are big compared to those of the electron and the atom’s
size, classical theory will be right. Where energies are
large and times long compared to atomic energies and
times, we shall not need to correct Newton. Where this is
so, the statistical laws of atomic physics will lead to proba-
bilities more and more like certitudes, and the acausal fea-
tures of atomic theory will be of no moment, and in fact
lost in the lack of precision with which questions about
large events will naturally be put.

In Bohr’s hands and those of the members of his school,
this correspondence principle was to prove a powerful

A SCIENCE IN CHANGE 49

tool. It did not say what the laws of atomic physics were,
but it said something about them. They must in this sense
be harmonious with, and ultimately reducible to, those of
large-scale physics. And when to this principle was added
the growing conviction that the laws of atomic physics
must deal not with the Newtonian position, velocity, and
acceleration that characterized a particle but with the ob-
servable features of atoms—the energies and properties
of stationary states, the probabilities of transitions between
these states—the groundwork was laid for the discovery
of quantum mechanics.

The principle of correspondence—this requirement that
the new laws of atomic mechanics should merge with those
of Newtonian mechanics for large bodies and events—thus
had great value as an instrument of discovery. Beyond
that, it illustrates the essential elements of the relation of
new discovery and old knowledge in science; the old
knowledge, as the very means for coming upon the new,
must in its old realm be left intact; only when we have left
that realm can it be transcended.

A discovery in science, or a new theory, even when it
appears most unitary and most all-embracing, deals with
some immediate element of novelty or paradox within the
framework of far vaster, unanalyzed, unarticulated re-
serves of knowledge, experience, faith, and presupposi-
tion. Our progress is narrow; it takes a vast world unchal-
lenged and for granted.

This is one reason why, however great the novelty or
scope of new discovery, we neither can, nor need, rebuild

50 SCIENCE AND THE COMMON UNDERSTANDING

the house of the mind very rapidly. This is one reason why
science, for all its revolutions, is conservative. This is why
we will have to accept the fact that no one of us really will
ever know very much. This is why we shall have to find
comfort in the fact that, taken together, we know more and

more.

ATOM AND VOID IN THE

THIRD MILLENNIUM

IN EXPLORING the atomic world, we have trav-
eled to a new country, strange for those who have lived in
the familiar world of Newtonian physics, strange even to
Newton’s own view of wonder and pre-vision. “God in the
Beginning,” he wrote, “form’d Matter in solid, massy,
hard, impenetrable, movable Particles. . . .”

We have our atoms; we are trying to understand them.
We have the simplest of the atoms, hydrogen, with a single
proton for its nucleus and a single electron to make it up.
But the ingredients do not follow Newton’s laws of motion.
Atoms of hydrogen appear to be all alike; they have a
fixed size; they are stable and not transitory; the light that
they emit is not what an electron circling in ever smaller
ellipses would radiate. They have a stability that does not
derive from Newtonian mechanics. When they are dis-
turbed by light or electrons or other matter, they take up
energy in definite quanta characteristic for the atom. They

52 SCIENCE AND THE COMMON UNDERSTANDING

are described in terms of states—states that are not orbits,
though they have some of the properties of some special
orbits. The states are stable, or almost stable. Transition
between them, occasioned by disturbance, or occurring
spontaneously with the emission of light, occurs by chance.
We do not know the cause of the individual transition but
only, at best, their probable distribution in time; nor do
we have, in terms of space and time and trajectory, any
picture whatever of what these transitions may be. These
acausal atoms compose the familiar world of large bodies,
orbits, and Newton’s laws. The laws that describe atomic
behavior, the stationary states and transitions, reduce by
correspondence, when applied to large systems, to New-
ton’s laws.

The discovery of these laws by Heisenberg could itself
have led to all we now know of quantum theory, but it was
supplemented as a matter of history by new discoveries in
related fields which make the task of understanding and
exposition simpler and more direct. Yet even these are
both unfamiliar and abstract; I fear that no exposition can
be wholly without difficulty,

Our problem has to do with the so-called duality of
wave and particle. On the one hand we have light, de-
scribed in detail as a continuous electromagnetic wave
with electric and magnetic fields, changing with a fre-
quency that determines the light’s color, and with an am-
plitude that determines its intensity. The waves of light

ATOM AND VOID IN THE THIRD MILLENNIUM 53

differ from radio waves only in one respect: their wave
length is much shorter. They differ obviously from the
waves we see on water, which are the more or less regular
displacement of matter. But when we talk here of waves,
in this account of wave-particle duality, as we shall have
to, it will mean something quite abstract, something com-
mon to light, radio, and water waves.

It will mean a state of affairs distributed in space and
propagating with time, sometimes a harmonic like a pure
note of sound and sometimes irregular like noise. It will
mean that these disturbances in general add, so that two
crests reinforce, and a crest and a trough tend to cancel. It
will mean that the sum of two effects may not be greater
than either, but smaller, as the phases of crest and trough
indicate. It will mean that, if we leave more than one al-
ternative for a particle or for light to go from one place to
another, the chance of arriving may be greater than the
sum of the chances or smaller than the sum of the chances,
because of this interference of the waves that represent the
alternatives.

When we deal with light, we deal with such waves; but
we also deal, as Einstein discovered, with something sharp,
discrete, and discontinuous—the light quantum. Whenever
light acts on matter, or is produced by it, we find packets
of defined energy and impulse, related to their frequency
and their wave number by the universal proportionality
of the quantum of action. How were these quanta to be
thought of? Were they guided by the waves? Were they
the waves? Were the waves an illusion, after all?

54 SCIENCE AND THE COMMON UNDERSTANDING

This turned out to be a universal quandary. De Broglie
suggested and later Davison found that there were waves
associated with electrons. Specifically Davison’s experi-
ment showed that electrons, too, when they are scattered by
the regular disturbance of a natural crystal, exhibit the
same signs of interference, the same unmistakable signa-
ture of the super-position of waves as light and as X-rays;
and later experiments showed that this is true of all the
other particles as well—protons, neutrons, and the atoms
themselves. It would be true of large objects also were it
not that their wave length is small, because of smallness of
Planck’s constant, and becomes completely insignificant
compared with their dimensions and with any practical
possibility of determining their location and outline.

All the questions which puzzled men about the relations
of Einstein’s quanta and Maxwell’s waves were thus to be
equally sharp and equally troublesome for the wave and
particle properties of matter. The resolution of these ques-
tions is the heart of atomic theory. They were brought to
the point of crisis by another great discovery—Schroedin-
ger’s discovery of his wave equation.

In its original, bold form this was the discovery of a
simple law for the propagation of electron waves—a natu-
ral generalization of the connection between wave number
and impulse, between energy and frequency, a generaliza-
tion nevertheless adequate to describe the gross features of
atomic systems and most of the familiar properties of mat-
ter. This equation had many sorts of solutions. Some were

ATOM AND VOID IN THE THIRD MILLENNIUM 55

stationary, unchanging in time, with a frequency and en-
ergy that corresponded to the stationary states of atoms.
This same equation had other solutions of a very different
kind, representing the trajectory of an electron as it might
be seen crossing the Wilson cloud chamber. It had still
other solutions, compounded by addition of several sta-
tionary states with their several proper frequencies. These
were not stationary but varied in time with frequencies
corresponding to the spectrum of atoms and molecules.

But what were these waves? What did they describe?
How were they related to the ways in which we observe
and study atomic systems, to Rutherford’s probings, to the
collisions and disturbances of atoms? Schroedinger under-
stood that in some sense the world of classical physics
would emerge from his equation, whenever the wave
lengths were small enough; then the trajectories for bodies
and planets would be like the geometric paths of light, the
rays of optics. But what would the waves mean when this
was not the case?

It would have been no answer to this question to attempt
to interpret the waves as an essentially mechanical disturb-
ance in some underlying mechanical medium; for the
questions which needed answering had to do with the prob-
lems of stationary states, and the behavior of electrons,
and not with a sub-stratum inaccessible to observation. Nor
was such a path followed. The discouraging outcome of an
analogous attempt with electromagnetic waves was conclu-
sive. It did not seem reasonable, nor in fact has it ever

56 SCIENCE AND THE COMMON UNDERSTANDING

proved possible, at a time when the very foundations of
classical mechanics were being altered, to reinterpret this
revolution in classical mechanical terms.

There was another false start. It was at one time sug-
gested that the waves, as they spread and moved, in some
sense represented the changing shape, extension, and flow
of the electron itself; when the disturbance grew larger the
electron grew larger; when the wave moved faster the elec-
tron moved faster. But to this interpretation there was an
insuperable obstacle. Whenever we looked for the position
of the particle, looked not directly with the eye, but with
the natural extension of looking with a microscope, we did
not find it spread out; we never found part of it in the
place where we were looking. Either it was there or it was
not there—the whole or none of it. Whenever we tried to
measure the velocity of an electron or its impulse, we
never found that part of it was moving with one speed and
part with another; there was always one electron, one ve-
locity, one answer to an experimental inquiry. The spread-
ing of the waves in space thus did not mean that the elec-
tron itself spread; it meant that the probability or likeli-
hood of our finding the electron, when we look for it,
spread as the wave does.

And thus it was that these waves were recognized as de-
scribing a state of affairs, as summarizing information we
had about the electron, as very much more abstract waves
indeed than we had hitherto encountered in physics. Their
interpretation was statistical as well as abstract: where a
disturbance was large, there we were likely to find the elec-

ATOM AND VOID IN THE THIRD MILLENNIUM 57

tron if we looked for it; where it was small, unlikely. If
the disturbance had ripples in which a certain wave length
was prominent, a measurement of the momentum would
be likely to give us a value corresponding to that wave
length. This clearly is qualitative talk. Quantitative rules
for assigning a wave function to describe the outcome of
an observation—or of other certain forms of knowledge,
such as that of an atom in its state of lowest energy—
needed to be, could be, and were developed; and they are
a part of quantum theory. Their exposition presupposes
some mathematical talk and calls at least for a blackboard.
Similarly, the simple rules which relate the magnitude or
properties of a wave function to the expectations that it
implies for one or another observation are a rigorous and
necessary part of the theory. But with these bonds to tie
the wave to our knowledge and to interpret it for our pre-
diction, the basis of the new physics has been laid.

It is a statistical physics, as indeed might have been ex-
pected from the statistical features of atomic transitions.
Its predictions are in the form of assertions of probability
and only rarely and specially in the form of certitudes.
With this in mind, let us look again at our problem of
interference, and of the two holes.

Let us think of an opaque screen with two holes in it.
Let us think of light, if we will; or, better still, let us think
of electrons of a given velocity and therefore a given wave
length and direction. We can do two experiments with a

58 SCIENCE AND THE COMMON UNDERSTANDING

source of electrons. In one, each hole in turn will be open
for a little, while the other is closed; in the other, both
holes will be open together. If we register the electrons on
the far side of the screen, for instance, with a photographic
plate, we see that the two patterns are radically different.
In the one case, we have a transmission through each of
the holes separately, with the characteristic diffraction
pattern for that wave length and for holes of that diameter.
These patterns are just added to one another on the photo-
graphic film. But if both holes are open at the same time,
something else happens. The waves that come through one
interfere with those that come through the other; spots that
were blackened before are now untouched and new spots
appear where the electrons do arrive.

If we try to think of this in terms of following the elec-
trons through one or the other of the holes, we cannot un-
derstand how it can make any difference whether that hole
through which the electron did not pass is open or shut; yet
it does. If we argue that the effect can be traced to the
interaction of electrons passing through the two holes, we
can disprove this by noting that the pattern is not affected
by reducing the number of electrons to the point where
there almost never are two passing through the two holes
at the same time. What we are observing is something char-
acteristic of the behavior of single particles, not of the
interaction of several.

Weare thus led to say that in this experiment a knowl-
edge of which hole the electron passed through is in princi-

ple inaccessible to us, that it is just the possibility of its

ATOM AND VOID IN THE THIRD MILLENNIUM 59

passing through one or the other that leads to the charac-
teristic new interference phenomena, the new light spots
and the new dark spots on the photographic film. We con-
clude that, if we should make provision for registering
through which hole the electron went, such as looking for
it or observing the small push that it gives to the screen as
it passes through, we would destroy the interference ef-
fects. We would then have the same result as if we had in
fact opened and shut the holes successively.

We see the connection between these conclusions and the
description of the state of affairs by a wave field in quali-
tative terms, rather closely paralleling the arguments that
were made quantitative in the uncertainty principle of
Heisenberg.

For we note that, if we were sure that the electron passed
through one of the holes, the wave field would have to be
restricted to that region; and that, if this were true, it
would have to be composed not of a single wave length, or
approximately a single one, but of waves of enough differ-
ent wave lengths so that they can reinforce each other at
one hole and vanish at the other; and we know that such
waves have lost the coherent quality necessary for inter-
ference. A little more generally, the waves of a single wave
length will correspond to an electron of a definite velocity
or impulse, but in an ill-defined or undefined position; the
waves that are localized to represent a definition of posi-
tion will be broadly scattered in wave length and represent
an undefined velocity or impulse. This complementary re-
striction on the degree to which a wave field can represent

60 SCIENCE AND THE COMMON UNDERSTANDING

both a well-defined position and a well-defined impulse is
universal; it is measured by the quantum of action. It
holds not only for electrons but for the more complicated
waves that describe complex systems, for atoms and nu-
clei and more composite bits of matter and more elemen-
tary ones. And the very fact that no wave field can give
that complete definition of the position and velocity of an
object which was taken for granted in classical physics is
also a description of the limitation on the observations
which in the real world we shall manage to make. It rep-
resents the fact that, when we study a system, making an
experiment or an observation on it, we may—and in gen-
eral we will, if we have prior knowledge before the experi-
ment—be losing in whole or in part that prior knowledge.
The experiment itself—that is, the physical] interactions
between the system and the equipment that we are using
to study it—will not only alter what we previously knew,
but will in general alter it in a way which cannot be fol-
lowed without invalidating the measurement or observa-
tion we have undertaken.

To cite but one example: if in the problem of the two
holes we try to detect which hole the electron has passed
through by noticing the push that it gives to the screen at
that point, we shall have to leave a part of the screen free
to respond to the push; and by this we lose all certitude as
to where that part of the screen was when that electron
passed through it. Many complex and detailed studies
have been made of how this limitation of knowledge oc-
curs in an experiment; but since the principle of comple-

ATOM AND VOID IN THE THIRD MILLENNIUM 61

mentarity, and the general adequacy of a wave field to
describe a state of affairs, underlies the description of
both the object and the instrument of observation, these
examples only illustrate and make vivid what must gener-
ally be true: the universal limitation, in contrast to classi-
cal physics, of the extent to which all aspects of a physical
system can be defined for the same system in the same
instance.

In observing atomic systems, in observing a system
where the finiteness of the quantum of action plays an
important part, we have a wide range of choice in the kind
of probe, the kind of experiment, the kind of experimental
equipment we wish to make. To any of these, if it is a good
experiment, there will be a meaningful answer which tells
us what the state of affairs is. From this, and from the
wave field which represents it, we can then make statistical
predictions of what will happen in a subsequent experi-
ment. The potentialities of measurement are varied. We
can do one thing or another; there are no inherent limits
on the choice of actions on the part of the observer.

This is a very different view of reality from Newton’s
giant machine. It is not causal; there is no complete causal
determination of the future on the basis of available
knowledge of the present. The application of the laws of
quantum theory restricts, but does not in general define,
the outcome of an experiment. This means that every ob-
servation on a system reveals some new knowledge as to
what its state is that did not exist before, and could not by
analysis and mathematical computation have been ob-

62 SCIENCE AND THE COMMON UNDERSTANDING

tained. It means that every intervention to make a meas-
urement, to study what is going on in the atomic world,
creates, despite all the universal order of this world, a
new, a unique, not fully predictable, situation.

Even in a brief account other points need to be men-
tioned. We have almost lost the concept of equations of
motion, having discovered that the very terms in which
they are formulated—position, velocity, acceleration, and
force—are not simultaneously applicable and do not,
taken together, correspond to things that we know about
the electron with enough accuracy to be meaningful for an
atomic system. Instead, what we can have is a knowledge
of the state, summarizing for us what we have found by
observation; and the analogue of the equation of motion
must tell us how, in response to forces acting within the
system or upon it, this state will change with time. This, it
turns out, is just what Schroedinger’s equation does. And
once again this equation, when applied to the familiar con-
texts of massive bodies and great distances, where the
quantum of action is in fact negligibly small, will describe
for us waves so reasonably concentrated in space, so little
dispersed about their average wave length, that the New-
tonian orbit reappears in its unaltered, classical path.

But this condition—this emergence of an orbit—is a
long way from the wave that describes the normal state
of an atom. State and orbit, like position and impulse, are
complementary notions; where one applies, the other can-

ATOM AND VOID IN THE THIRD MILLENNIUM 63

not be defined, and for a full description we must be able
to use now one, now the other, depending on the observa-
tion and the questions that we put.

When we speak here of observer and object, of instru-
ment or probe, and system to be probed, we are not talk-
ing of the mind of man. We are talking of a division
between the object of study and the means used to study
it. That division can be made in more than one way. We
may regard the a-particles that Rutherford used as an in-
strument, and their response as a measure of the state of
affairs. We may regard the a-particle as a part of the sys-
tem we are studying, and the slits that define its path or
the fields that deflect it and the screens that detect it as the
instrument. But whichever we do, the observation will al-
ways be transformed into some large-scale happening—
some flash of light, some triggering of a circuit, some
pointing of a pointer on the dial of an instrument—which
is well defined and familiar and unambiguous, and where
the question of our freedom to do one or another observa-
tion on it no longer is relevant. The atomic world has not
lost its objective quality; but it attains this by means of
those interlockings with experiment which we use to define
one or another of its properties and to measure them.

It needs to be clear that what is described here is
not an expression of mood or preference or taste; it is
an exact, beautiful, quantitative, immensely versatile,
and immensely successful science. It is what students
learn when they prepare themselves for further re-
searches in physics, or what engineers learn whose

64 SCIENCE AND THE COMMON UNDERSTANDING

engineering involves a knowledge of the solid state of
physical materials, or what chemists learn if they wish to
understand the subtler features of chemical bonding or
chemical kinetics, or astronomers if they wish to know
what things are like in the interior of the stars. One could
go much farther in describing this discipline, even without
mathematics; but the words would before long become
cumbersome and unfamiliar and almost a misinterpreta-
tion of what in mathematical terms can be said with beauty
and simplicity.

Even some of the more paradoxical features of quantum
theory turn out to be related to practical matters of real
importance. One of the earliest to be noted and the oddest
is this: if, in familiar life, we roll a ball up a hill and it
does not have enough vigor to get over the top, it will roll
back on the same side; it will not get through the hill. But
if we bombard sucha hill with a-particles or electrons they
may have a small chance of getting through, even when
they cannot get over. This has a close analogy with the fact
that very small objects do not cast sharp shadows in a
beam of light. Light because of its wave nature bends
around them. It corresponds to the fact that when we let
electrons or other particles of definite energy encounter
a barrier, neither the kinetic nor the potential energy alone
can be completely well defined; and indeed, were we to
try to detect the electron just as it passes through the hill,
we should need an experiment that could give the electron

ATOM AND VOID IN THE THIRD MILLENNIUM 65

enough energy to be quite legitimately on top of the hill.
This penetration of barriers is not without importance. It
accounts for the fact that the a-particles that Rutherford
used could sometimes, after millions of years, escape from
the nuclei through a high hill where electrostatic repulsion
had imprisoned them. It accounts for the fact that in the
sun and other stars nuclei having only very moderate en-
ergy occasionally come into contact and react. Thus the
stars light the heavens, and the sun warms and nourishes
the earth.

Another consequence of the wave-like character of all
matter is that, when particles with very low velocity and
very long wave length bombard other particles of matter,
they may interact far more often than if these interactions
were limited to their coming in contact. The very lack of
definition of their relative position makes interaction pos-
sible, in some cases over distances characterized not by
their dimensions but by their wave length. This is the cir-
cumstance which, among many others, enables the rare
Uranium-235, as it occurs in natural uranium, to catch up
enough of the neutrons which fly about to sustain a chain
reaction in an atomic reactor.

There are even some odd things about the identity and
the identifiability of the electrons themselves. That they
are all similar we know. Their inherent properties, their
charge, their mass when at rest, are the same. We wish that
we understood this better; some day, no doubt, we shall;
but we know that it is true. But if classical physics were
the whole story, we could still, if we wished, always iden-

66 SCIENCE AND THE COMMON UNDERSTANDING

tify an electron, and know that it was the same as the one
we had seen before. We could follow it, not, it is true,
without trouble, but without paradox, without inconsist-
ency, from where we first found it through its collisions
and interactions and deflections and changes by keeping
in touch with its trajectory. If it hit another electron, we
would know which it was that came out in one direction
and which in another. In fact this is not really true, except
in those special instances where the collision is of such low
energy that the two electrons can be described by waves
which never overlap at the same place at the same time. As
soon as that is no longer the case, we lose in principle all
ability to tell one electron from another; and in atomic
physics, where the electrons of an atom, and even the elec-
trons of neighboring atoms, are not well defined in position
and can often occupy the same volume, we have no way
of identifying the individual particle. This, too, has con-
sequences. When two electrons collide, the wave that rep-
resents one of them and the wave that represents the other
may, and do, interfere; and this gives rise to novel effects
and new forms for the interactions produced by their elec-
tric repulsion. It is responsible for the permanent magnet-
ism of magnets. It is responsible for the bonding of or-
ganic chemistry and for the very existence in any form
that we can readily imagine of living matter and of life
itself.

These examples are not given to perplex and bemuse.
They are rather illustrations of how even the most para-
doxical and unexpected consequences of the new mechan-

ATOM AND VOID IN THE THIRD MILLENNIUM 67

ics, of wave-particle duality, and of complementarity are
involved in an understanding of important and familiar
features of the natural world, and of how massive is the
system of understanding and knowledge of which they are
a part.

UNCOMMON SENSE

A CENTURY after Newton, in 1784, the progress
of that century was celebrated in an anonymous memorial
lodged in the ball of the tower of St. Margaret’s church at
Gotha, to be found by men of future times. It read:

“Our days have been the happiest time of the eight-
eenth century. . . . Hatred born of dogma and the com-
pulsion of conscience sink away; love of man and freedom
of thought gain the upper hand. The arts and sciences blos-
som, and our vision into the workshop of nature goes deep.
Artisans approach artists in perfection; useful skills flower
at all levels. Here you have a faithful portrait of our time.
. . » Do the same for those who come after you and re-
joice!”

Transience is the backdrop for the play of human prog-
ress, for the improvement of man, the growth of his know]-
edge, the increase of his power, his corruption and his

UNCOMMON SENSE 69

partial redemption. Our civilizations perish; the carved
stone, the written word, the heroic act fade into a memory
of memory and in the end are gone. The day will come
when our race is gone; this house, this earth in which we
live will one day be unfit for human habitation, as the sun
ages and alters.

Yet no man, be he agnostic or Buddhist or Christian,
thinks wholly in these terms. His acts, his thoughts, what
he sees of the world around him—the falling of a leaf or a
child’s joke or the rise of the moon—are part of history;
but they are not only part of history; they are a part of
becoming and of process but not only that: they partake
also of the world outside of time; they partake of the light
of eternity.

These two ways of thinking, the way of time and history
and the way of eternity and of timelessness, are both part
of man’s effort to comprehend the world in which he lives.
Neither is comprehended in the other nor reducible to it.
They are, as we have learned to say in physics, comple-
mentary views, each supplementing the other, neither tell-
ing the whole story. Let us return to this.

First, we had best review and extend somewhat this
account of the complementarity of the physicists. In its
simplest form it is that an electron must sometimes be
considered as a wave, and sometimes as a particle—a
wave, that is, with the continuous propagation and char-
acteristic interference that we learn to understand in the

7O SCIENCE AND THE COMMON UNDERSTANDING

optics laboratory, or as a particle, a thing with well-de-
fined location at any time, discrete and individual and
atomic. There is this same duality for all matter and for
light. In a little subtler form this complementarity means
that there are situations in which the position of an atomic
object can be measured and defined and thought about
without contradiction; and other situations in which this
is not so, but in which other qualities, such as the energy
or the impulse of the system, are defined and meaningful.
The more nearly appropriate the first way of thinking is to
a situation, the more wholly inappropriate the second, so
that there are in fact no atomic situations in which both
impulse and position will be defined well enough to permit
the sort of prediction with which Newtonian mechanics has
familiarized us.

It is not only that when we have made an observation on
a system and determined, let us say, its position, we do not
know its impulse. That is true, but more than that is true.
We could say that we know the position of that system and
that it may have any one of a number of different im-
pulses. If we try on that basis to predict its behavior as a
sort of average behavior of all objects which have the
measured position and which have different and unmeas-
ured impulses, and work out the average answer according
to Newton’s laws, we get a result that is wholly at variance
with what we find in nature. This is because of the peculiar
property, which has no analogue in the mechanics of large
objects, of interference between waves representing the
consequences of assuming one impulse and those of assum-

UNCOMMON SENSE 71

ing another. We are not, that is, allowed to suppose that
position and velocity are attributes of an atomic system,
some of which we know and others of which we might know
but do not. We have to recognize that the attempt to dis-
cover these unknown attributes would lose for us the
known; that we have a choice, a disjunction; and that this
corresponds to the different ways we can go about observ-
ing our atom or experimenting with it.

We have a state of affairs completely defined by the
nature of the observation and by its outcome—the nature
determining what properties of the system will be well de-
fined in the state and what poorly. The outcome then is the
determination of the well-defined quantities by measure-
ment. This state thus is a summary, symbolic and uncom-
fortably abstract for general exposition, of what sort of
observation we have made and what we have found
through it. It codifies those characteristics of the experi-
mental arrangement which are reliable, in the sense that
the equipment we use records something that we know
about atomic systems. It describes also those character-
istics that are indeterminate, in the sense that they may not
only have been disturbed or altered, but that their disturb-
ance cannot be registered or controlled without the loss, in
the experiment, of all ability to measure what was sup-
posed to be measured.

This state, this description of the atom, is not the only
way of talking about it. It is the only way appropriate to
the information we have and the means that we have used
to obtain it. It is the full account of this information; and

72 SCIENCE AND THE COMMON UNDERSTANDING

if the experiment was properly and scrupulously done it
tells us all that we can find out. It is not all that we could
have found out had we chosen a different experiment. It is
all that we could find out having chosen this.

This state is objective. We can calculate its properties,
reproduce it with similar atoms on another occasion, verify
its properties and its ways of change with time. There is no
element of the arbitrary or subjective. Once we have done
our experiment and its result is recorded and the atom
disengaged, we know its meaning and its outcome; we can
then forget the details of how we got our information.

But, although the state of the system is objective, a
mechanical picture of how it was brought into being is not
generally possible. There is a most vivid example of this,
made famous by the prominent part it played in the de-
bates between Einstein and Bohr as to the meaning and
adequacy of atomic theory. It can be put rather simply.
Let us suppose that we have two objects; one of them may
be an electron or an atom, and it will be the one we wish
to study. The other may be a relatively large piece of
matter—a screen with a hole through it, or any other
body; but it should be heavy so that its motion will be
unimportant compared to that of the electron. Let us sup-
pose that we by measurement know the impulse or mo-
mentum of both of these objects, and have them collide.
Let the electron go through the hole, or bounce off the
other body. If, after the collision, we measure the impulse
of the heavy body, we will then know that of the electron
because, as Newton’s third law teaches us, the sum of the

UNCOMMON SENSE 73

impulses is not altered by the collision. In that case we
would have a state of the electron of well-defined impulse,
as precisely defined as we had made the precision of our
measurements. If, on the other hand, we observed the posi-
tion of the heavy body, we would know where the light one
had been at the moment of the collision, and so would have
a quite different description of its state, one in which its
position and not its impulse had been well defined—or, in
the language of waves, a spherical wave with its center at
the point of collision, and not a plane wave with its direc-
tion and wave length corresponding to the momentum.

We have thus the option of realizing one or the other of
two wholly dissimilar states for the electron, by a choice of
what we observe about the heavy body with which it once
was in interaction. We are not, in any meaningful sense,
physically altering or qualifying the electron; we are de-
fining a part of, although in this case a late part of, the
experimental procedure, the very nature of the experiment
itself. If we exercise neither option, if we let the heavy
body go with unmeasured momentum and undefined posi-
tion, then we know nothing of the electron at all. It has no
state, and we are not prepared to make any meaningful
predictions of what will become of it or of what we shall
find should we again attempt an experiment upon it. The
electron cannot be objectified in a manner independent of
the means chosen for observing or studying it. The only
property we can ascribe to it without such consideration
is our total ignorance.

This is a sharp reminder that ways of thinking about

74 SCIENCE AND THE COMMON UNDERSTANDING

things, which seem natural and inevitable and almost ap-
pear not to rest on experience so much as on the inherent
qualities of thought and nature, do in fact rest on experi-
ence; and that there are parts of experience rendered ac-
cessible by exploration and experimental refinement where
these ways of thought no longer apply.

It is important to remember that, if a very much subtler
view of the properties of an electron in an atomic system
is necessary to describe the wealth of experience we have
had with such systems, it all rests on accepting without
revision the traditional accounts of the behavior of large-
scale objects. The measurements that we have talked about
in such highly abstract form do in fact come down in the
end to looking at the position of a pointer, or the reading
of time on a watch, or measuring out where on a photo-
graphic plate or a phosphorescent screen a flash of light or
a patch of darkness occurs. They all rest on reducing the
experience with atomic systems to experiment and observa-
tion made manifest, unambiguous, and objective in the be-
havior of large objects, where the precautions and incerti-
tudes of the atomic domain no longer directly apply. So it
is that ever-increasing refinements and critical revisions in
the way we talk about remote or small or inaccessible parts
of the physical world have no direct relevance to the fa-
miliar physical world of common experience.

Common sense is not wrong in the view that it is mean-
ingful, appropriate, and necessary to talk about the large

UNCOMMON SENSE 75

objects of our daily experience as though they had a veloc-
ity that we knew, and a place that we knew, and all the rest
of it. Common sense is wrong only if it insists that what is
familiar must reappear in what is unfamiliar. It is wrong
only if it leads us to expect that every country that we
visit is like the last country we saw. Common sense, as the
common heritage from the millennia of common life, may
lead us into error if we wholly forget the circumstances to
which that common life has been restricted.

Misunderstanding of these relations has led men to wish
to draw from new discoveries, and particularly those in the
atomic domain, far-reaching consequences for the ordi-
nary affairs of men. Thus it was noted that, since the ulti-
mate laws of atomic behavior are not strictly causal, not
strictly determinate, the famous argument of Laplace for
a wholly determinate universe could not be maintained.
And there were men who believed that they had discovered
in the acausal and indeterminate character of atomic
events the physical basis for that sense of freedom which
characterizes man’s behavior in the face of decision and
of responsibility.

In a similar light-hearted way it was pointed out that,
as the state of an atomic system requires observation for
its definition, so the course of psychological phenomena
might be irretrievably altered by the very effort to probe
them—as a man’s thoughts are altered by the fact that he
has formulated and spoken them. It is, of course, not the
fact that observation may change the state of an atomic
system that gives rise to the need for a complementary

76 SCIENCE AND THE COMMON UNDERSTANDING

description; it is the fact that, if the observation is to be
meaningful, it will preclude any analysis or control of that
change, that is decisive.

But these misapplications of the findings of atomic phys-
ics to human affairs do not establish that there are no valid
analogies. These analogies will, in the nature of things, be
less sharp, less compelling, less ingenious. They will rest
upon the fact that complementary modes of thought and
complementary descriptions of reality are an old, long-
enduring part of our tradition. All that the experience of
atomic physics can do in these affairs is to give us a re-
minder, and a certain reassurance, that these ways of talk-
ing and thinking can be factual, appropriate, precise, and
free of obscurantism.

There are a number of examples which are illuminated
by, and in turn illuminate, the complementarity of atomic
theory. Some of them are from quite different parts of
human life and some of them from older parts of science.
There is one from physics itself which is revealing, both
in its analogies and its points of difference. One of the
great triumphs of nineteenth-century physics was the ki-
netic theory of heat—what is called statistical mechanics.
This is both an interpretation and a deduction of many of
the large-scale properties and tendencies of matter: of the
tendency, for instance, of bodies that can exchange heat to
come to a common temperature, or of the density of a gas
to be uniform throughout a container, or of work to dis-
sipate itself in heat, or quite generally of all of those ir-
reversible processes in nature wherein the entropy of

UNCOMMON SENSE 77

systems increases, and forms become more uniform and
less differentiated when left to themselves to develop.
The phenomena we deal with here are defined in terms
of temperature and density and pressure and other large-
scale properties. The kinetic theory, statistical mechanics,
interprets the behavior of these systems in terms of the
forces acting on the molecules and of the motion of the
molecules that compose them, which are usually quite ac-
curately described by Newton’s laws. But it is a statistical
theory of this motion, recognizing that in fact we do not
in general know, and are not in detail concerned with, the
positions and velocities of the molecules themselves, but
only with their average behavior. We interpret the temper-
ature of a gas, for instance, in terms of the average kinetic
energy of its molecules, and the pressure as the average of
the forces exerted by the collision of these molecules on
the surface of the container. This description in terms of
averages, embodying as part of itself our ignorance of the
detailed state of affairs, is thus in some sense complemen-
tary to a complete dynamic description in terms of the
motion of the individual molecules. In this sense kinetic
theory and dynamics are complementary. One applies to a
situation in which the individual patterns of molecular be-
havior are known and studied; the other applies to a situ-
ation largely defined by our ignorance of these patterns.
But the analogy to atomic complementarity is only par-
tial, because there is nothing in the classical dynamics
which underlies kinetic theory to suggest that the behavior
of a gas would be any different if we had performed the

78 SCIENCE AND THE COMMON UNDERSTANDING

immense job of locating and measuring what all the mole-
cules were doing. We might then, it is true, not find it
natural to talk about temperature, because we would need
no average behavior; we would have an actual one; but
we could still define the temperature in terms of the total
kinetic energy of the molecules, and we would still find
that it tended to equalize between one part of the system
and another.

We have therefore a situation in which there are two
ways of describing a system, two sets of concepts, two
centers of preoccupation. One is appropriate when we are
dealing with a very few molecules and want to know what
those molecules do; the other appropriate when we have a
large mass of matter and only rough and large-scale ob-
servations about it.

There is, however, no logical or inherent difficulty
within the framework of classical physics, in combining
both descriptions for a single system—and classical phys-
ics, we repeat, is adequate for most, if not all, of these
problems of statistical mechanics. It is not that we cannot
do this without violating the laws of physics; it is that it
makes no sense to do it, since each description is appropri-
ate to a context quite different from the other. It is clear
that, if we insisted on the detailed description of the mo-
tion of individual molecules, the notions of probability
which turn out to be so essential for our understanding of
the irreversible character of physical events in nature
would never enter. We should not have the great insight
that we now do: namely, that the direction of change in the
world is from the less probable to the more, from the more

UNCOMMON SENSE 79

organized to the less, because all we would be talking
about would be an incredible number of orbits and trajec-
tories and collisions. It would be a great miracle to us that,
out of equations of motion, which to every allowed motion
permit a precisely opposite one, we could nevertheless
emerge into a world in which there is a trend of change
with time which is irreversible, unmistakable, and fa-

miliar in all our physical experience.

In considering the relations between the various
sciences, there are similar instances of complementary
views. In many cases, it is not clear whether this is the sort
of complementarity that we have between the statistical
and dynamic descriptions of a gas, a contrast of interest
and terminology, but not an inherent inapplicability of
two ways of talking; or whether on the contrary the situa-
tion is in fact more as it is in atomic physics, where the
nature of the world is such that the two modes of descrip-
tion cannot be applied at once to the same situation. Every
science has its own language. But dictionaries of transla-
tion between the languages do exist, and mark an ever-
growing understanding and unity of science as a whole.
It is not always clear whether the dictionaries will be
complete; between physics and chemistry they apparently
are. Everything the chemist observes and describes can be
talked about in terms of atomic mechanics, and most of it
at least can be understood. Yet no one suggests that, in
dealing with the complex chemical forms which are of
biological interest, the language of atomic physics would
be helpful. Rather it would tend to obscure the great

80 SCIENCE AND THE COMMON UNDERSTANDING

regularities of biochemistry, as the dynamic description
of a gas would obscure its thermodynamic behavior.

The contrast becomes even more marked when we con-
sider the physico-chemical description of living forms.
Here, in spite of the miraculous sharpness of the tools of
chemical analysis, of the extensive use not only of the
microscope but of the electron microscope to determine
fine details of biological structure, in spite of the use of
tracers to follow changes on a molecular scale, questions
have still been raised as to whether this description can
in the nature of things be complete.

The question involves two points: the first having to do
with the impossibility of wholly isolating a biological sys-
tem from its physical environment without killing it; the
second with the possibility that a really complete physico-
chemical study of the pivotal structures in biological proc-
esses—of genes, let us say, in the nuclei of dividing cells
—might not be incompatible with the undisturbed course
of life itself. It would appear to be the general opinion of
biologists that no such limitations will prove decisive; that
a complete description of biology will be possible not only
in terms of the concepts of biology but in terms reducible
to those of physics and chemistry. Certainly it is a large
part of the aim and wonder of biological progress to carry
this program as far as possible.

Analogous questions appear much sharper, and their
answer more uncertain, when we think of the phenomena
of consciousness; and, despite all the progress that has
been made in the physiology of the sense organs and of
the brain, despite our increasing knowledge of these in-

UNCOMMON SENSE 81

tricate marvels both as to their structure and their func-
tioning, it seems rather unlikely that we shall be able to
describe in physico-chemical terms the physiological
phenomena which accompany a conscious thought, or
sentiment, or will. Today the outcome is uncertain. What-
ever the outcome, we know that, should an understanding
of the physical correlate of elements of consciousness in-
deed be available, it will not itself be the appropriate
description for the thinking man himself, for the clarifica-
tion of his thoughts, the resolution of his will, or the de-
light of his eye and mind at works of beauty. Indeed, an
understanding of the complementary nature of conscious
life and its physical interpretation appears to me a lasting
element in human understanding and a proper formula-
tion of the historic views called psycho-physical paral-
lelism.

For within conscious life, and in its relations with the
description of the physical world, there are again many
examples. There is the relation between the cognitive and
the affective sides of our lives, between knowledge or
analysis and emotion or feeling. There is the relation be-
tween the aesthetic and the heroic, between feeling and
that precursor and definer of action, the ethical commit-
ment; there is the classical relation between the analysis
of one’s self, the determination of one’s motives and pur-
poses, and that freedom of choice, that freedom of deci-
sion and action, which are complementary to it.

Whether a physico-chemical description of the material
counterpart of consciousness will in fact ever be possible,
whether physiological or psychological observation will

82 SCIENCE AND THE COMMON UNDERSTANDING

ever permit with any relevant confidence the prediction of
our behavior in moments of decision and in moments of
challenge, we may be sure that these analyses and these
understandings, even should they exist, will be as irrele-
vant to the acts of decision and the castings of the will as
are the trajectories of molecules to the entropy of a gas.
To be touched with awe, or humor, to be moved by beauty,
to make a commitment or a determination, to understand
some truth—these are complementary modes of the human
spirit. All of them are part of man’s spiritual life. None
can replace the others, and where one is called for the
others are in abeyance.

Just as with the a-particles of Rutherford, which were
first for him an object of study and then became for him
a tool of study, a tool for investigating other objects, so
our thoughts and words can be the subject of reflection and
analysis; so we can be introspective, critical, and full of
doubt. And so, in other times and other contexts, these
same words, these same thoughts taken as instruments, are
the power of human understanding itself, and the means of
our further enlightenment.

The wealth and variety of physics itself, the greater
wealth and variety of the natural sciences taken as a whole,
the more familiar, yet still strange and far wider wealth
of the life of the human spirit, enriched by complemen-
tary, not at once compatible ways, irreducible one to the
other, have a greater harmony. They are the elements of
man’s sorrow and his splendor, his frailty and his power,
his death, his passing, and his undying deeds.

THE SCIENCES

AND MAN’S COMMUNITY

FOR some moments during these lectures we have
looked together into one of the rooms of the house called
“science.”” This is a relatively quiet room that we know as
quantum theory or atomic theory. The great girders which
frame it, the lights and shadows and vast windows—these
were the work of a generation our predecessor more than
two decades ago. It is not wholly quiet. Young people visit
it and study in it and pass on to other chambers; and from
time to time someone rearranges a piece of the furniture
to make the whole more harmonious; and many, as we
have done, peer through its windows or walk through it
as sight-seers. It is not so old but that one can hear the
sound of the new wings being built nearby, where men
walk high in the air to erect new scaffoldings, not uncon-
scious of how far they may fall. All about there are busy
workshops where the builders are active, and very near
indeed are those of us who, learning more of the primor-

84 SCIENCE AND THE COMMON UNDERSTANDING

dial structure of matter, hope some day for chambers as
fair and lovely as that in which we have spent the years of
our youth and our prime.

It is a vast house indeed. It does not appear to have
been built upon any plan but to have grown as a great city
grows. There is no central chamber, no one corridor from
which all others debouch. All about the periphery men are
at work studying the vast reaches of space and the state of
affairs billions of years ago; studying the intricate and
subtle but wonderfully meet mechanisms by which life
proliferates, alters, and endures; studying the reach of the
mind and its ways of learning; digging deep into the atoms
and the atoms within atoms and their unfathomed order.
It is a house so vast that none of us know it, and even the
most fortunate have seen most rooms only from the out-
side or by a fleeting passage, as in a king’s palace open
to visitors. It is a house so vast that there is not and need
not be complete concurrence on where its chambers stop
and those of the neighboring mansions begin.

It is not arranged in a line nor a square nor a circle nor
a pyramid, but with a wonderful randomness suggestive
of unending growth and improvisation. Not many people
live in the house, relatively speaking—perhaps if we count
all its chambers and take residence requirements quite
lightly, one tenth of one per cent, of all the people in this
world—probably, by any reasonable definition, far fewer.
And even those who live here live elsewhere also, live in
houses where the rooms are not labelled atomic theory or
genetics or the internal constitution of the stars, but quite

THE SCIENCES AND MAN’S COMMUNITY 85

different names like power and production and evil and
beauty and history and children and the word of God.

We go in and out; even the most assiduous of us is not
bound to this vast structure. One thing we find throughout
the house: there are no locks; there are no shut doors;
wherever we go there are the signs and usually the words
of welcome. It is an open house, open to all comers.

The discoveries of science, the new rooms in this great
house, have changed the way men think of things outside
its walls. We have some glimmering now of the depth in
time and the vastness in space of the physical world we
live in. An awareness of how long our history and how
immense our cosmos touches us even in simple earthly
deliberations. We have learned from the natural history of
the earth and from the story of evolution to have a sense of
history, of time and change. We learn to talk of ourselves,
and of the nature of the world and its reality as not wholly
fixed in a silent quiet moment, but as unfolding with nov-
elty and alteration, decay and new growth. We have under-
stood something of the inner harmony and beauty of
strange primitive cultures, and through this see the qualli-
ties of our own life in an altered perspective, and recog-
nize its accidents as well as its inherent necessities. We
are, I should think, not patriots less but patriots very
differently for loving what is ours and understanding a
little of the love of others for their lands and ways. We
have begun to understand that it is not only in his rational
life that man’s psyche is intelligible, that even in what may
appear to be his least rational actions and sentiments we

86 SCIENCE AND THE COMMON UNDERSTANDING

may discover a new order. We have the beginnings of an
understanding of what it is in man, and more in simple
organisms, that is truly heritable, and rudimentary clues
as to how the inheritance occurs. We know, in surprising
detail, what is the physical counterpart of the act of vision
and of other modes of perception. Not one of these new
ideas and new insights is so little, or has so short a reach
in its bearing on the common understanding but that it
alone could make a proper theme for “Science and the
Common Understanding.” Yet we have been, bearing in
mind my limited area of experience, in that one room of
the part of the house where physics is, in which I have
for some years worked and taught.

In that one room—in that relatively quiet room where
we have been together—we have found things quite
strange for those who have not been there before, yet
reminiscent of what we have seen in other houses and
known in other days. We have seen that in the atomic
world we have been led by experience to use descriptions
and ideas that apply to the large-scale world of matter, to
the familiar world of our schoolday physics; ideas like
the position of a body and its acceleration and its impulse
and the forces acting on it; ideas like wave and interfer-
ence; ideas like cause and probability. But what is new,
what was not anticipated a half-century ago, is that, though
to an atomic system there is a potential applicability of
one or another of these ideas, in any real situation only
some of these ways of description can be actual. This is
because we need to take into account not merely the atomic

THE SCIENCES AND MAN’S COMMUNITY 87

system we are studying, but the means we use in observing
it, and the fitness of these experimental means for defining
and measuring selected properties of the system. All such
ways of observing are needed for the whole experience of
the atomic world; all but one are excluded in any actual
experience. In the specific instance, there is a proper and
consistent way to describe what the experience is; what it
implies; what it predicts and thus how to deal with its
consequences. But any such specific instance excludes by
its existence the application of other ideas, other modes of
prediction, other consequences. They are, we say, com-
plementary to one another; atomic theory is in part an
account of these descriptions and in part an understanding
of the circumstances to which one applies, or another or
another.

And so it is with man’s life. He may be any of a number
of things; he will not be all of them. He may be well
versed, he may be a poet, he may be a creator in one or
more than one science; he will not be all kinds of man or
all kinds of scientist; and he will be lucky if he has a bit
of familiarity outside the room in which he works.

So it is with the great antinomies that through the ages
have organized and yet disunited man’s experience: the
antinomy between the ceaseless change and wonderful
novelty and the perishing of all earthly things, and the
eternity which inheres in every happening; in the an-
tinomy between growth and order, between the spontane-
ous and changing and irregular and the symmetrical and
balanced; in the related antinomy between freedom and

88 SCIENCE AND THE COMMON UNDERSTANDING

necessity ; between action, the life of the will, and observa-
tion and analysis and the life of reason; between the ques-
tion “how?” and the questions “why?” and “to what
end?’’; between the causes that derive from natural law,
from unvarying regularities in the natural world, and
those other causes that express purposes and define goals
and ends.

So it is in the antinomy between the individual and the
community; man who is an end in himself and man whose
tradition, whose culture, whose works, whose words have
meaning in terms of other men and his relations to them.
All our experience has shown that we can neither think,
nor in any true sense live, without reference to these anti-
nomic modes. We cannot in any sense be both the observ-
ers and the actors in any specific instance, or we shall fail
properly to be either one or the other; yet we know that
our life is built of these two modes, is part free and part
inevitable, is part creation and part discipline, is part ac-
ceptance and part effort. We have no written rules that
assign us to these ways; but we know that only folly and
death of the spirit results when we deny one or the other,
when we erect one as total and absolute and make the
others derivative and secondary. We recognize this when
we live as men. We talk to one another; we philosophize;
we admire great men and their moments of greatness; we
read; we study; we recognize and love in a particular act
that happy union of the generally incompatible. With all

THE SCIENCES AND MAN’S COMMUNITY 89

of this we learn to use some reasonable part of the full
register of man’s resources.

We are, of course, an ignorant lot; even the best of us
knows how to do only a very few things well; and of what
is available in knowledge of fact, whether of science or of
history, only the smallest part is in any one man’s know-
ing.

The greatest of the changes that science has brought is
the acuity of change; the greatest novelty the extent of
novelty. Short of rare times of great disaster, civilizations
have not known such rapid alteration in the conditions of
their life, such rapid flowering of many varied sciences,
such rapid changes in the ideas we have about the world
and one another. What has been true in the days of a great
disaster or great military defeat for one people at one
time is true for all of us now, in the sense that our ends
have little in common with our beginnings. Within a life-
time what we learned at school has been rendered inade-
quate by new discoveries and new inventions; the ways
that we learn in childhood are only very meagerly ade-
quate to the issues that we must meet in maturity.

In fact, of course, the notion of universal knowledge has
always been an illusion; but it is an illusion fostered by
the monistic view of the world in which a few great central
truths determine in all its wonderful and amazing prolif-
eration everything else that is true. We are not today
tempted to search for these keys that unlock the whole of
human knowledge and of man’s experience. We know that
we are ignorant; we are well taught it, and the more

go SCIENCE AND THE COMMON UNDERSTANDING

surely and deeply we know our own job the better able
we are to appreciate the full measure of our pervasive
ignorance. We know that these are inherent limits, com-
pounded, no doubt, and exaggerated by that sloth and that
complacency without which we would not be men at all.

But knowledge rests on knowledge; what is new is mean-
ingful because it departs slightly from what was known
before; this is a world of frontiers, where even the live-
liest of actors or observers will be absent most of the time
from most of them. Perhaps this sense was not so sharp in
the village—that village which we have learned a little
about but probably do not understand too well—the vil-
lage of slow change and isolation and fixed culture which
evokes our nostalgia even if not our full comprehension.
Perhaps in the villages men were not so lonely; perhaps
they found in each other a fixed community, a fixed and
only slowly growing store of knowledge—a single world.
Even that we may doubt, for there seem to be always in the
culture of such times and places vast domains of mystery,
if not unknowable, then imperfectly known, endless and
open.

As for ourselves in these times of change, of ever-in-
creasing knowledge, of collective power and individual
impotence, of heroism and of drudgery, of progress and of
tragedy, wetoo are brothers. And if we, who are the inher-
itors of two millennia of Christian tradition, understand

that for us we have come to be brothers second by being

THE SCIENCES AND MAN’S COMMUNITY g1

children first, we know that in vast parts of the world
where there has been no Christian tradition, and with men
who never have been and never may be Christian in faith
there is nevertheless a bond of brotherhood. We know
this not only because of the almost universal ideal of
human brotherhood and human community; we know it at
first hand from the more modest, more diverse, more fleet-
ing associations which are the substance of our life. The
ideal of brotherhood, the ideal of fraternity in which all
men, wicked and virtuous, wretched and fortunate, are
banded together has its counterpart in the experience of
communities, not ideal, not universal, imperfect, imper-
manent, as different from the ideal and as reminiscent of
it as are the ramified branches of science from the ideal of
a unitary, all-encompassing science of the eighteenth cen-
tury.

Each of us knows from his own life how much even a
casual and limited association of men goes beyond him in
knowledge, in understanding, in humanity, and in power.
Each of us, from a friend or a book or by concerting of
the little we know with what others know, has broken the
iron circle of his frustration. Each of us has asked help
and been given it, and within our measure each of us has
offered it. Each of us knows the great new freedom sensed
almost as a miracle, that men banded together for some
finite purpose experience from the power of their common
effort. We are likely to remember the times of the last war,
where the common danger brought forth in soldier, in
worker, in scientist, and engineer a host of new experi-

g2 SCIENCE AND THE COMMON UNDERSTANDING

ences of the power and the comfort in even bleak under-
takings, of common, concerted, co-operative life. Each of
us knows how much he has been transcended by the group
of which he has been or is a part; each of us has felt the
solace of other men’s knowledge to stay his own ignorance,
of other men’s wisdom to stay his folly, of other men’s
courage to answer his doubts or his weakness.

These are the fluid communities, some of long duration
when circumstances favored—like the political party or
many a trade union—some fleeting and vivid, encompass-
ing in the time of their duration a moment only of the
member’s life; and in our world at least they are ramified
and improvised, living and dying, growing and falling off
almost as a form of life itself. This may be more true of
the United States than of any other country. Certainly the
bizarre and comical aspects impressed de Tocqueville
more than a century ago when he visited our land and com-
mented on the readiness with which men would band to-
gether: to improve the planting of a town, or for political
reform, or for the pursuit or inter-exchange of knowledge,
or just for the sake of banding together, because they
liked one another or disliked someone else. Circumstances
may have exaggerated the role of the societies, of the fluid
and yet intense communities in the United States; yet these
form a common pattern for our civilization. It brought
men together in the Royal Society and in the French
Academy and in the Philosophical Society that Franklin
founded, in family, in platoon, ona ship, in the laboratory,
in almost everything but a really proper club.

THE SCIENCES AND MAN’S COMMUNITY 93

If we err today—and I think we do—it is in expecting
too much of knowledge from the individual and too much
of synthesis from the community. We tend to think of these
communities, no less than of the larger brotherhood of
man, as made up of individuals, as composed of them as
an atom is of its ingredients. We think similarly of general
laws and broad ideas.as made up of the instances which
illustrate them, and from an observation of which we may
have learned them.

Yet this is not the whole. The individual event, the act,
goes far beyond the general law. It is a sort of intersection
of many generalities, harmonizing them in one instance as
they cannot be harmonized in general. And we as men are
not only the ingredients of our communities; we are their
intersection, making a harmony which does not exist be-
tween the communities except as we, the individual men,
may create it and reveal it. So much of what we think, our
acts, our judgments of beauty and of right and wrong,
come to us from our fellow men that what would be left
were we to take all this away would be neither recogniza-
ble nor human. We are men because we are part of, but
not because only part of, communities; and the attempt to
understand man’s brotherhood in terms only of the indi-
vidual man is as little likely to describe our world as is the
attempt to describe general laws as the summary of their
instances. These are indeed two complementary views,
neither reducible to the other, no more reducible than is
the electron as wave to the electron as particle.

And this is the mitigant of our ignorance. It is true that

94 SCIENCE AND THE COMMON UNDERSTANDING

none of us will know very much; and most of us will see
the end of our days without understanding in all its detail
and beauty the wonders uncovered even in a single branch
of a single science. Most of us will not even know, as a
member of any intimate circle, anyone who has such
knowledge; but it is also true that, although we are sure
not to know everything and rather likely not to know very
much, we can know anything that is known to man, and
may, with luck and sweat, even find out some things that
have not before been known to him. This possibility,
which, as a universal condition of man’s life is new, repre-
sents today a high and determined hope, not yet a reality;
it is for us in England and in the United States not wholly
remote or unfamiliar. It is one of the manifestations of our
belief in equality, that belief which could perhaps better
be described as a commitment to unparalleled diversity
and unevenness in the distribution of attainments, knowl-
edge, talent, and power.

This open access to knowledge, these unlocked doors
and signs of welcome, are a mark of a freedom as funda-
mental as any. They give a freedom to resolve difference
by converse, and, where converse does not unite, to let
tolerance compose diversity. This would appear to be a
freedom barely compatible with modern political tyranny.
The multitude of communities, the free association for
converse or for common purpose, are acts of creation. It
is not merely that without them the individual is the
poorer; without them a part of human life, not more nor
less fundamental than the individual, is foreclosed. It is a

THE SCIENCES AND MAN’S COMMUNITY 95

cruel and humorless sort of pun that so powerful a present
form of modern tyranny should call itself by the very
name of a belief in community, by a word “communism”
which in other times evoked memories of villages and vil-
lage inns and of artisans concerting their skills, and of
men of learning content with anonymity. But perhaps
only a malignant end can follow the systematic belief that
all communities are one community; that all truth is one
truth; that all experience is compatible with all other; that
total knowledge is possible; that all that is potential can
exist as actual. This is not man’s fate; this is not his path;
to force him on it makes him resemble not that divine
image of the all-knowing and all-powerful but the help-
less, iron-bound prisoner of a dying world. The open
society, the unrestricted access to knowledge, the un-
planned and uninhibited association of men for its further-
ance—these are what may make a vast, complex, ever-
growing, ever-changing, ever more specialized and expert
technological world nevertheless a world of human com-

munity.

So it is with the unity of science—that unity that is far
more a unity of comparable dedication than a unity of
common total understanding. This heartening phrase, “the
unity of science,” often tends to evoke a wholly false pic-
ture, a picture of a few basic truths, a few critical tech-
niques, methods, and ideas, from which all discoveries

and understanding of science derive; a sort of central ex-

96 SCIENCE AND THE COMMON UNDERSTANDING

change, access to which will illuminate the atoms and the
galaxies, the genes and the sense organs. The unity of
science is based rather on just such a community as I have
described. All parts of it are open to all of us, and this is
no merely formal invitation. The history of science is rich
in example of the fruitfulness of bringing two sets of tech-
niques, two sets of ideas, developed in separate contexts
for the pursuit of new truth, into touch with one another.
The sciences fertilize each other; they grow by contact and
by common enterprise. Once again, this means that the
scientist may profit from learning about any other science;
it does not mean that he must learn about them all. It
means that the unity is a potential unity, the unity of the
things that might be brought together and might throw
light one on the other. It is not global or total or hier-
archical.

Even in science, and even without visiting the room in
its house called atomic theory, we are again and again
reminded of the complementary traits in our own life,
even in our own professional life. We are nothing without
the work of others our predecessors, others our teachers,
others our contemporaries. Even when, in the measure of
our adequacy and our fullness, new insight and new order
are created, we are still nothing without others. Yet we
are more.

There is a similar duality in our relations to wider
society. For society our work means many things: pleas-
ure, we hope, for those who follow it; instruction for those
who perhaps need it; but also and far more widely, it

THE SCIENCES AND MAN’S COMMUNITY 97

means a common power, a power to achieve that which
could not be achieved without knowledge. It means the
cure of illness and the alleviation of suffering; it means
the easing of labor and the widening of the readily acces-
sible frontiers of experience, of communication, and of
instruction. It means, in an earthy way, the power of better-
ment—that riddled word. We are today anxiously aware
that the power to change is not always necessarily good.

As new instruments of war, of newly massive terror,
add to the ferocity and totality of warfare, we understand
that it is a special mark and problem of our age that man’s
ever-present preoccupation with improving his lot, with
alleviating hunger and poverty and exploitation, must be
brought into harmony with the over-riding need to limit
and largely to eliminate resort to organized violence be-
tween nation and nation. The increasingly expert destruc-
tion of man’s spirit by the power of police, more wicked if
not more awful than the ravages of nature’s own hand, is
another such power, good only if never to be used.

We regard it as proper and just that the patronage of
science by society is in large measure based on the in-
creased power which knowledge gives. If we are anxious
that the power so given and so obtained be used with wis-
dom and with love of humanity, that is an anxiety we
share with almost everyone. But we also know how little
of the deep new knowledge which has altered the face of
the world, which has changed—and increasingly and ever
more profoundly must change—man’s views of the world,
resulted from a quest for practical ends or an interest in

98 SCIENCE AND THE COMMON UNDERSTANDING

exercising the power that knowledge gives. For most of
us, in most of those moments when we were most free of
corruption, it has been the beauty of the world of nature
and the strange and compelling harmony of its order, that
has sustained, inspirited, and led us. That also is as it
should be. And if the forms in which society provides and
exercises its patronage leave these incentives strong and
secure, new knowledge will never stop as long as there are
men.

We know that our work is rightly both an instrument
and an end. A great discovery is a thing of beauty; and
our faith—our binding, quiet faith—is that knowledge is
good and good in itself. It is also an instrument; it is an
instrument for our successors, who will use it to probe else-
where and more deeply; it is an instrument for technology,
for the practical arts, and for man’s affairs. So it is with
us as scientists; so it is with us as men. We are at once
instrument and end, discoverers and teachers, actors and
observers. We understand, as we hope others understand,
that in this there is a harmony between knowledge in the
sense of science, that specialized and general knowledge
which it is our purpose to uncover, and the community of
man. We, like all men, are among those who bring a little
light to the vast unending darkness of man’s life and
world. For us as for all men, change and eternity, special-
ization and unity, instrument and final purpose, com-
munity and individual man alone, complementary each
to the other, both require and define our bonds and our
freedom.

NOTE

The six chapters of this book are the Reith Lectures given
over the home service of the British Broadcasting Corpora-
tion in November and December, 1953. They are printed es-
sentially as broadcast. I have added two appendixes.

In the one I have collected the texts from which brief
quotation is made in the lectures. The texts seem to me of
interest in themselves; and in any case, this is the surest way
to correct any distortion or color which my abbreviation may
have introduced. In some cases the texts may even prompt
curiosity to read further.

In the second appendix, I have given a brief and informal
bibliography on atomic theory and its interpretation.

J. R. O.

APPENDIX I

SIR ISAAC NEWTON
(Page 12)

All these things being consider’d, it seems probable to me,
that God in the Beginning form’d Matter in solid, massy,
hard, impenetrable, moveable Particles, of such Sizes and
Figures, and with such other Properties, and in such Propor-
tion to Space, as most conduced to the End for which he
form’d them; and that these primitive Particles being Solids,
are incomparably harder than any porous Bodies compounded
of them; even so very hard, as never to wear or break in
pieces; no ordinary Power being able to divide what God him-
self made one in the first Creation. While the Particles con-
tinue entire, they may compose Bodies of one and the same Na-
ture and Texture in all Ages: But should they wear away, or
break in pieces, the Nature of Things depending on them,
would be changed. Water and Earth, composed of old worn
Particles and Fragments of Particles, would not be of the
same Nature and Texture now, with Water and Earth com-
posed of entire Particles in the Beginning. And therefore,
that Nature may be lasting, the Changes of corporeal Things

SCIENCE AND THE COMMON UNDERSTANDING 103

are to be placed only in the various Separations and new
Associations and Motions of these permanent Particles; com-
pound Bodies being apt to break, not in the midst of solid
Particles, but where those Particles are laid together, and
only touch in a few Points.

It seems to me farther, that these Particles have not only a
Vis inerte, accompanied with such passive Laws of Motion
as naturally result from that Force, but also that they are
moved by certain active Principles, such as is that of Gravity,
and that which causes Fermentation, and the Cohesion of
Bodies. These Principles I consider, not as occult Qualities,
supposed to result from the specifick Forms of Things, but
as general Laws of Nature, by which the Things themselves
are form’d; their Truth appearing to us by Phenomena,
though their Causes be not yet discover’d. . . .

Sir Isaac Newton, Opticks (New York: Dover
Publications, Inc., 1952), Book 3, Part I, Query
31, p. 400. Based on the Fourth Edition, London,
1730.

THOMAS SPRAT
(Page 16)

I will here, in the first place, contract into few Words, the
whole Sum of their Resolutions; which I shall often have
occasion to touch upon in Parcels. Their Purpose is, in short,
to make faithful Records of all the Works of Nature, or Art,
which can come within their Reach; that so the present Age,
and Posterity, may be able to put a Mark on the Errors,
which have been strengthned by long Prescription; to restore
the Truths, that have lain neglected; to push on those, which
are already known, to more various Uses; and to make the
way more passable, to what remains unreveal’d. This is the
Compass of their Design. And to accomplish this, they have
endeavour’d, to separate the Knowledge of Nature, from the
Colours Rhetorick, the Devices of Fancy, or the delightful
Deceit of Fables. They have labor’d to inlarge it, from being
confin’d to the Custody of a few, or from Servitude to private
Interests. They have striven to preserve it from being over-
press’d by a confus’d Heap of vain and useless Particulars;
or from being streightned and bound too much up by general

SCIENCE AND THE COMMON UNDERSTANDING 105

Doctrines. They have tried to put it into a Condition of per-
petual Increasing; by settling an inviolable Correspondence
between the Hand and the Brain. They have studied, to make
it not only an Enterprise of one Season, or of some lucky
Opportunity; but a Business of Time; a steady, a lasting, a
popular, an uninterrupted Work. They have attempted, to
free it from the Artifice, and Humors, and Passions of Sects;
to render it an Instrument, whereby Mankind may obtain a
Dominion over Things, and not only over one another’s Judg-
ments: And lastly, they have begun to establish these Refor-
mations in Philosophy, not so much, by any solemnity of
Laws, or Ostentation of Ceremonies, as by solid Practice and
Examples; not by a glorious Pomp of Words; but by the si-
lent, effectual, and unanswerable Arguments of real Produc-
tions.

This will more fully appear, by what I am to say on these
four Particulars, which shall make up this Part of my Rela-
tion, the Qualifications of their Members; the Manner of their
Inquiry; their Weekly Assemblies; and their Way of Reg-
istring.

As for what belongs to the Members themselves that are to
constitute the Society: It is to be noted, that they have freely
admitted Men of different Religions, Countries, and Profes-
sions of Life. This they were oblig’d to do, or else they would
come far short of the Largeness of their own Declarations.
For they openly profess, not to lay the Foundation of an Eng-
lish, Scotch, Irish, Popish, or Protestant Philosophy; but a
Philosophy of Mankind.

That the Church of England ought not to be apprehensive
of this free Converse of various Judgments, I shall afterwards
manifest at large. For the present, I shall frankly assert, that

106 APPENDIX I

our Doctrine, and Discipline, will be so far from receiving
Damage by it; that it were the best Way to make them uni-
versally embrac’d, if they were oftner brought to be canvass’d
amidst all Sorts of Dissenters. It is dishonorable, to pass a
hard Censure on the Religions of all other Countries: It con-
cerns them, to look to the Reasonableness of their Faith; and
it is sufficient for us, to be establish’d in the Truth of our own.

Thomas Sprat, The History of the Royal Society of
London (3rd ed.; London, 1722), pp. 61-63.

THOMAS JEFFERSON
(Page 18)

Monticello June 18. 99.
DEAR SIR,

I have to acknolege the reciept of your favor of May 14.
in which you mention that you have finished the 6. first books
of Euclid, plane trigonometry, surveying and algebra and
ask whether I think a further pursuit of that branch of science
would be useful to you. There are some propositions in the
latter books of Euclid, and some of Archimedes, which are
useful, and I have no doubt you have been made acquainted
with them. Trigonometry, so far as this, is most valuable to
every man, there is scarcely a day in which he will not resort
to it for some of the purposes of common life; the science of
calculation also is indispensible as far as the extraction of
the square and cube roots; Algebra as far as the quadratic
equation and the use of logarithms are often of value in ordi-
nary cases: but all beyond these is but a luxury; a delicious
luxury indeed; but not to be indulged in by one who is to
have a profession to follow for his subsistence. In this light

108 APPENDIX I

I view the conic sections, curves of the higher orders, perhaps
even spherical trigonometry, Algebraical operations beyond
the 2d dimension, and fluxions. There are other branches of
science however worth the attention of every man: Astron-
omy, botany, chemistry, natural philosophy, natural history,
anatomy. Not indeed to be a proficient in them; but to pos-
sess their general principles and outlines, so as that we may
be able to amuse and inform ourselves further in any of them
as we proceed through life and have occasion for them. Some
knowlege of them is necessary for our character as well as
comfort. The general elements of astronomy and of natural
philosophy are best acquired at an academy where we can
have the benefit of the instruments and apparatus usually
provided there: but the others may well be acquired from
books alone as far as our purposes require. I have indulged
myself in these observations to you, because the evidence
cannot be unuseful to you of a person who has often had
occasion to consider which of his acquisitions in science have
been really useful to him in life, and which of them have been
merely a matter of luxury.

I am among those who think well of the human character
generally. I consider man as formed for society, and endowed
by nature with those dispositions which fit him for society.
I believe also, with Condorcet, as mentioned in your letter,
that his mind is perfectible to a degree of which we cannot
as yet form any conception. It is impossible for a man who
takes a survey of what is already known, not to see what an
immensity in every branch of science yet remains to be dis-
covered, and that too of articles to which our faculties seem
adequate. In geometry and calculation we know a great deal.
Yet there are some desiderata. In anatomy great progress has

SCIENCE AND THE COMMON UNDERSTANDING 109

been made; but much is still to be acquired. In natural his-
tory we possess knowlege; but we want a great deal. In chem-
istry we are not yet sure of the first elements. Our natural
philosophy is in a very infantine state; perhaps for great ad-
vances in it, a further progress in chemistry is necessary.
Surgery is well advanced; but prodigiously short of what may
be. The state of medecine is worse than that of total ignor-
ance. Could we divest ourselves of every thing we suppose
we know in it, we should start from a higher ground and with
fairer prospects. From Hippocrates to Brown we have had
nothing but a succession of hypothetical systems each having
it’s day of vogue, like the fashions and fancies of caps and
gowns, and yielding in turn to the next caprice. Yet the hu-
man frame, which is to be the subject of suffering and torture
under these learned modes, does not change. We have a few
medecines, as the bark, opium, mercury, which in a few well
defined diseases are of unquestionable virtue: but the resid-
uary list of the materia medica, long as it is, contains but the
charlataneries of the art; and of the diseases of doubtful form,
physicians have ever had a false knowlege, worse than ignor-
ance. Yet surely the list of unequivocal diseases and remedies
is capable of enlargement; and it is still more certain that in
the other branches of science, great fields are yet to be ex-
plored to which our faculties are equal, and that to an extent
of which we cannot fix the limits. I join you therefore in
branding as cowardly the idea that the human mind is in-
capable of further advances. This is precisely the doctrine
which the present despots of the earth are inculcating, and
their friends here re-echoing; and applying especially to re-
ligion and politics; ‘that it is not probable that any thing
better will be discovered than what was known to our fathers.”

110 APPENDIX I

We are to look backwards then and not forwards for the im-
provement of science, and to find it amidst feudal barbarisms
and the fires of Spital-fields. But thank heaven the American
mind is already too much opened, to listen to these impos-
tures; and while the art of printing is left to us, science can
never be retrograde; what is once acquired of real knowlege
can never be lost. To preserve the freedom of the human
mind then and freedom of the press, every spirit should be
ready to devote itself to martyrdom; for as long as we may
think as we will, and speak as we think, the condition of man
will proceed in improvement. The generation which is going
off the stage has deserved well of mankind for the struggles
it has made, and for having arrested that course of despotism
which had overwhelmed the world for thousands and thou-
sands of years. If there seems to be danger that the ground
they have gained will be lost again, that danger comes from
the generation your cotemporary. But that the enthusiasm
which characterises youth should lift it’s parracide hands
against freedom and science would be such a monstrous
phaenomenon as | cannot place among possible things in this
age and this country. Your college at least has shewn itself
incapable of it; and if the youth of any other place have
seemed to rally under other banners it has been from de-
lusions which they will soon dissipate. I shall be happy to
hear from you from time to time, and of your progress in
study, and to be useful to you in whatever is in my power;
being with sincere esteem Dear Sir

Your friend & servt

Th: Jefferson

Scripta Mathematica, I (1932), 88-90.

THOMAS HOBBES
(Page 21)

Good successe is Power; because it maketh reputation of
Wisdome, or good fortune; which makes men either feare
him, or rely on him.

Affability of men already in power, is encrease of Power;
because it gaineth love.

Reputation of Prudence in the conduct of Peace or War, is
Power; because to prudent men, we commit the government
of our selves, more willingly than to others.

Nobility is Power, not in all places, but onely in those
Common-Wealths, where it has Priviledges: for in such
priviledges consisteth their Power.

Eloquence is power; because it is seeming Prudence.

Forme is Power; because being a promise of Good, it rec-
ommendeth men to the favour of women and strangers.

The Sciences, are small Power; because not eminent; and
therefore, not acknowledged in any man; nor are at all, but in
a few; and in them, but of a few things. For Science is of that
nature, as none can understand it to be, but such as in a good

measure have attayned it.

112 APPENDIX I

Arts of publique use, as Fortification, making of Engines,
and other Instruments of War; because they conferre to De-
fence, and Victory, are Power: And though the true Mother
of them, be Science, namely the Mathematiques; yet, because
they are brought into the Light, by the hand of the Artificer,
they be esteemed (the Midwife passing with the vulgar for
the Mother,) as his issue.

Thomas Hobbes, Leviathan, ed. by A. R. Waller
(“Cambridge English Classics”; Cambridge:
Cambridge University Press, 1904), Part I, Chap.
10, pp. 54-55.

INSCRIPTION ON STEEPLE
KNOB OF ST. MARGARET'S
CHURCH AT GOTHA

(Page 68)

Unsere Tage fiillten den gliicklichsten Zeitraum des acht-
zehnten Jahrhunderts. Kaiser, Kénige, Fiirsten steigen von
ihrer gefiirchteten Hohe menschenfreundlich herab, vera-
chten Pracht und Schimmer, werden Vater, Freunde und
Vertraute ihres Volks. Die Religion zerreisst das Pfaffenge-
wand und tritt in ihrer Gottlichkeit hervor. Aufklarung geht
mit Riesenschritten. Tausende unserer Briider und Schwe-
stern, die in geheiligter Unthatigkeit lebten, werden dem
Staat geschenkt. Glaubenshass und Gewissenszwang sinken
dahin; Menschenliebe und Freiheit im Denken gewinnen die
Oberhand. Kinste und Wissenschaften bliihen, und tief drin-
gen unsere Blicke in die Werkstatt der Natur. Handwerker
nahern sich gleich den Kiinstlern der Vollkommenheit, niitz-
liche Kenntnisse Keimen in allen Standen. Hier habt Ihr eine
getreue Schilderung unserer Zeit. Blickt nicht stolz auf uns
herab, wenn Ihr hcher steht und weiter seht als wir; erkennt
vielmehr aus dem gegebenen Gemilde, wie sehr wir mit Muth

114 APPENDIX I

und Kraft Euren Standort emporhoben und stiitzten. Thut
fir Eure Nachkommenschaft ein Gleiches und seid gliicklich!

Our days have been the happiest time of the eighteenth
century. Emperors, kings and princes step down from their
feared heights, and as friends of men scorn pomp and glitter
and become fathers, friends and confidants of their people.
Religion tears off its popish garb and stands forth in its di-
vinity. Enlightenment advances with giant steps. Thousands
of our brothers and sisters who previously spent their lives in
holied idleness are given back to the community. Hatred born
of dogma and the compulsion of conscience sink away; love
of man and freedom of thought gain the upper hand. The arts
and sciences blossom, and our vision into the workshop of
nature goes deep. Artisans approach artists in perfection;
useful skills flower at all levels. Here you have a faithful por-
trait of our time. Look not proudly down upon us, should you
stand higher or see farther than we, but rather recognize from
this picture how with courage and strength we raised and
supported your standard. Do the same for those who come
after you and rejoice!

Hermann Hettner, Literaturgeschichte des Acht-
zehnten Jahrhunderts, Vol. III (Braunschweig:
Friederich Vieweg und Sohn, 1879), Book 2,
Chap. 1, p. 171.

ALEXIS DE TOCQUEVILLE

(Page 92)

DE L’USAGE QUE LES AMERICAINS FONT DE
L’ASSOCIATION DANS LA VIE CIVILE

Je ne veux point parler de ces associations politiques a
aide desquelles les hommes cherchent a4 se défendre contre
Yaction despotique d’une majorité ou contre les empiéte-
ments du pouvoir royal. J’ai déja traité ce sujet ailleurs. I]
est clair que si chaque citoyen, a mesure qu’il devient indivi-
duellement plus faible, et par conséquent plus incapable de
préserver isolément sa liberté, n’apprenait pas I’art de s’unir
a ses semblables pour la défendre, la tyrannie croitrait né-
cessairement avec l’égalité. I] ne s’agit ici que des associa-
tions qui se forment dans la vie civile, et dont l’objet n’a rien
de politique.

Les associations politiques qui existent aux Etats-Unis ne
forment qu’un détail au milieu de l’immense tableau que
l’ensemble des associations y présente.

Les Américains de tous les ages, de toutes les conditions, de
tous les esprits, s’unissent sans cesse. Non-seulement ils ont
des associations commerciales et industrielles auxquelles tous
prennent part, mais ils en ont encore de mille autres espéces:
de religieuses, de morales, de graves, de futiles, de fort géné-

116 APPENDIX I

rales et de trés-particuliéres, d’immenses et de fort petites; les
Américains s’associent pour donner des fétes, fonder des sé-
minaires, batir des auberges, élever des églises, répandre des
livres, envoyer des missionaires aux antipodes; ils créent de
cette maniére des hdpitaux, des prisons, des écoles. S’agit-il
enfin de mettre en lumiére une vérité, ou de développer un
sentiment par l’appui d’un grand exemple: ils s’associent.
Partout oi, a la téte d’une entreprise nouvelle, vous voyez en
France le gouvernement, et en Angleterre un grand seigneur,
comptez que vous apercevrez aux Etats-Unis une association.
J’ai rencontré en Amérique des sortes d’associations dont
je confesse que je n’avais pas méme lidée, et j’ai souvent
admiré l’art infini avec lequel les habitants des Etats-Unis
parvenaient a fixer un but commun aux efforts d’un grand
nombre d’hommes, et a les faire marcher librement.

OF THE USE WHICH THE AMERICANS MAKE OF
PUBLIC ASSOCIATIONS IN CIVIL LIFE

I do not propose to speak of those political associations by
the aid of which men endeavor to defend themselves against
the despotic action of a majority or against the aggressions of
regal power. That subject I have already treated. If each
citizen did not learn, in proportion as he individually be-
comes more feeble and consequently more incapable of pre-
serving his freedom singlehanded, to combine with his fel-
low citizens for the purpose of defending it, it is clear that
tyranny would unavoidably increase together with equality.

Only those associations that are formed in civil life without
reference to political objects are here referred to. The politi-
cal associations that exist in the United States are only a
single feature in the midst of the immense assemblage of asso-

SCIENCE AND THE COMMON UNDERSTANDING 117

ciations in that country. Americans of all ages, all conditions,
and all dispositions constantly form associations. They have
not only commercial and manufacturing companies, in which
all take part, but associations of a thousand other kinds, re-
ligious, moral, serious, futile, general or restricted, enormous
or diminutive. The Americans make associations to give en-
tertainments, to found seminaries, to build inns, to construct
churches, to diffuse books, to send missionaries to the an-
tipodes; in this manner they found hospitals, prisons, and
schools. If it is proposed to inculcate some truth or to foster
some feeling by the encouragement of a great example, they
form a society. Wherever at the head of some new under-
taking you see the government in France, or a man of rank
in England, in the United States you will be sure to find an
association.

I met with several kinds of associations in America of
which I confess I had no previous notion; and I have often
admired the extreme skill with which the inhabitants of the
United States succeed in proposing a common object for the
exertions of a great many men and in inducing them volun-
tarily to pursue it.

Alexis de Tocqueville, De la Démocratie en Amé-
rique, Vol. III (14iéme édition; Paris: Michel
Levy Fréres, 1864), Deuxiéme Partie, Chap. 2,
p. 175. English translation from Alexis de Tocque-
ville, Democracy in America, Vol. I] (New York:
Alfred A. Knopf, 1948), Book 2, Chap. 5, p. 106.

APPENDIX II

Chapters Two to Five deal at some length with atomic
theory and with some of the experiments that underlie it.
With the exception of contemporary work on the “new parti-
cles,” there are many admirable technical text books and
monographs.

As for Chapter Two, the interested reader may wish to
turn to the classic texts of E. R. Rutherford, Radioactive
Substances and their Radiations (Cambridge: Cambridge
University Press; New York: Putnam; 1913), and to Ruther-
ford, Chadwick, and Ellis, Radiations from Radioactive Sub-
stances (Cambridge: Cambridge University Press, 1930).
The “new particles” were discussed at a conference held at
Bagnéres de Bigorre, July, 1953. The record of this confer-
ence, issued by the Ecole Polytechnique, Paris, gives a most
vivid impression of the present state of knowledge, ignor-
ance, and progress. Even for those who do not wish to con-
sult the proceedings of the conference, the comment follow-
ing the title may be of interest: “Les particules décrites au
cours de ce Congrés ne sont pas entiérement fictives, et toute

SCIENCE AND THE COMMON UNDERSTANDING 119

analogie avec des particules existant dans la nature n’est pas
une pure coincidence.”

There are numerous good technical texts on the quantum
mechanics, the quantum theory of atoms. In particular I
recommend:

P. A. M. Dirac. The Principles of Quantum Mechanics. Ox-

ford: Clarendon Press, 1930.
W. Pauli. “Die Allgemeinen Prinzipien der Wellenmecha-
nik,” Handbuch der Physik, XXIV (1933), 1, 83.
L. I. Schiff. Quantum Mechanics. New York: McGraw-Hill
Book Co., 1949.
Of these, Schiff’s text is the most elementary.

No attempt has been made in the lectures to give a full
historic account of the contributions made to the develop-
ment of quantum theory. Where names have been mentioned,
it is because they have become generally identified with
principles or with theories; but any account of the history
of quantum theory should at least mention Born, Dirac, and
Pauli, in addition to the names that occur in the text.

As to the interpretation of quantum theory, these may
serve to guide the reader should he want more detailed,
more original, and more substantive accounts of the matters
touched on in the lectures:

W. Heisenberg. The Physical Principles of the Quantum

Theory. Chicago: University of Chicago Press, 1930.
N. Bohr. Atomic Theory and the Description of Nature.
New York: (Cambridge University Press) The Mac-
millan Co., 1934.

N. Bohr. “On the Notions of Causality and Complementar-
ity,” Dialectica, II (1948), 312.

120 APPENDIX II

N. Bohr. “Discussion with Einstein on Epistemological
Problems in Atomic Physics,” Albert Einstein, Philoso-
pher-Scientist. Edited by P. A. Schilpp. “Library of
Living Philosophers”; Evanston, Illinois, 1949.

W. Pauli. “Die philosophische Bedeutung der Idee der
Komplementaritat,” Experientia, VI (1950), 72.

ABOUT THE AUTHOR

J. RopertT OPPENHEIMER has been director of the Institute
for Advanced Study at Princeton, New Jersey, since 1947. He
is a physicist trained at Harvard, Cambridge and Gottingen,
who has been a professor at the University of California and
at the California Institute of Technology. Between 1943 and
1945 he was director of the laboratory at Los Alamos in New

Mexico, where the first atomic bombs were made.